Kwa wale wakali wa Algebra, Solve this

[Myomb_0]

Another brain teaser: A water tank reservoir is connected to three water pipe supplies, pipes a, b and c. Pipe a alone can fill the tank in 30 minutes while pipe b can fill it in 45 minutes and pipe c alone can fill it in 90 minutes. How long will the reservoir tank fill up if all water pipes are opened to the tank at the same time.

[(V/30)+(V/45)+(V/90)]t=V

6/90=1/t ==> t=15

Itachukua 15 minutes.

 

[Joselela]

U Have Been Awarded A Trophy , , Kula Tano Mkuu Umenikumbusha Mbali Sana

Hahaha au sio kitambo mbaya...
Thanks for the award, mods mnipe trophy aisee!!!

 

[Joselela]

Sawa kabisa! Hongera

Shukrani sana, hongera pia!

 

[Maji Baridi]

Nataka kuigilizia majibu hapa
=4829

 

[kilambimkwidu]

Na sisi wakali wa kusahau PIN tunazishe thread yetu

 

[nard]

Dah.....meaningless...... Vipi kama dakika zingekuwa 31,43 and 91? Unatakiwa ujue physical quantities.... volume...flow rate and time

Nimekubali ila nadhani njia yangu ingeleta shida kubwa sana kwa msahishaji. Kikubwa yanatakiwa kutungwa maswali ambayo hayawezi kuleta mkanganyiko, mfano maswali ya variations shule ya msingi yanatungwa kwa namna ambayo mwanafunzi akitumia njia yenye umbo kama "W" anapata jibu kitu ambacho ni tofauti kwa mwanafunzi wa sekondari!

 

[Makanyaga]

Another brain teaser: A water tank reservoir is connected to three water pipe supplies, pipes a, b and c. Pipe a alone can fill the tank in 30 minutes while pipe b can fill it in 45 minutes and pipe c alone can fill it in 90 minutes. How long will the reservoir tank fill up if all water pipes are opened to the tank at the same time.

Naomba nijibu hili swali katika namna ambayo hata yule ambaye hajui hesabu atatelewa.

BOMBA A lina uwezo wa kujaza TANK kwa muda wa dakika 30. Kwa hiyo lina uwezo wa kujaza 1/30 ya tank kwa muda wa dakika 1, na kwa maana hiyo basi:

BOMBA A litajza 1/30 ya TANK kwa muda wa dakika 1


BOMBA B litajza 1/45 ya TANK kwa muda wa dakika 1

BOMBA C litajza 1/90 ya TANK kwa muda wa dakika 1

Mabomba yote matatu yatajaza (1/30) + (1/45) + (1/90) = 1/15 kwa muda wa dakika 1! (siyo dakika 3 tafadhali)

Kwa hiyo kama mabomba matatu yanaweza kujaza 1/15 ya TANK kwa muda wa dakika 1, then yana uwezo wa kujaza 15/15 ya TANK kwa muda wa dakika 1x15= dakika 15

Hivyo mabomba yote matatu yatajaza TANK hilo kwa muda wa dakika 15.

MUHIMU:
Hili swali limekaa katika mfumo wa applied/ business mathematics zaidi, yaani mahesabu ambayo yanatumiwa na watu katika shughuli za maisha za kila siku kama vile kwenye business. Na kama ni Chuo Kikuu, swali la mfumo wa namna hii anatkiwa aulizwe sana sana mtu anayesoma digrii kama vile ya Bachellor of Commerce au Engineering, na si mtu anayesoma let's say degree ya mahesabu perce. Hivyo unapofikia hatua ya kuli-solve kwa kutumia KDS na KKS (GCF and the like), unakuwa uko sahihi katika jibu, ila kwenye njia yako ya kufikia jawabu kidogo inakuwa ina mgogoro ukizingatia nature ya swali lenyewe.

Still, swali hili liko katika kiwango cha chini sana kuweza kuulizwa katika ngazi hizo nilizozitaja na nakumbuka kama wakati enzi hizo wakati sisi wazee tunasoma shule za msingi, maswali ya aina hii yalikuwa yanapatikana katika kitabu kimoja maarufu sana kilikuwa kinaenda kwa jina la: JIANDAE VEMA KUMALIZA ELIMU YA SHULE YA MSINGI, manuscript iliyokuwa popular sana enzi hizo kwa wanafunzi wa shule za msingi na tulikuwa tunakatiza kwa kuiita "JIANDAE". Ilikuwa ni enzi hizo miaka ya 1947 wakati tuku shule za msingi, enzi za mkoloni.

 

[Nematic]

GCF of 30, 45 and 90 = 15
The tank will be filled after 15 minutes

Ukiongeza bomba jingine linaloweza kujaza kwa dk 60, GCF is still 15, hapo je?

 

[Nematic]

Mkuu umepata. Ila ungeonyesha njia kama ifuatavyo: let time taken to fill the tank be t. Therefore t/30+t/45+t/90 = 1
Solving for t we have 6t/90 = 1.

Therefore t = 90/6 = 15.

Time taken to fill the tanks=15

Maswali ya rate huwa yanasumbua wakati mwingine.
Hebu tusaidie hili:

Tank la lita 50 limewekewa mchanganyiko wa maji na chumvi(soluble, kipimo/concentration ya 30 gramu/lita) kiasi cha lita 25 zimejazwa.
Kuna bomba limefunguliwa linaweka maji kwenye tank kiasi cha lita 3 kwa dakika na hapo hapo kuna mrija/tobo kwenye tank linachuruzisha maji kutoka kwenye tank kiasi cha lita 1¼ kwa dakika.

a) Tanki litajaa baada ya muda gani?
b) mchanganyiko wa kwenye tanki utasomaje wakati likijaa?

 

[Nematic]

[(V/30)+(V/45)+(V/90)]t=V

6/90=1/t ==> t=15

Itachukua 15 minutes.

V imebeba umuhimu upi hapa, iko virtual kabisa

 

[Nematic]

Naomba nijibu hili swali katika namna ambayo hata yule ambaye hajui hesabu atatelewa.

BOMBA A lina uwezo wa kujaza TANK kwa muda wa dakika 30. Kwa hiyo lina uwezo wa kujaza 1/30 ya tank kwa muda wa dakika 1, na kwa maana hiyo basi:

BOMBA A litajza 1/30 ya TANK kwa muda wa dakika 1


BOMBA B litajza 1/45 ya TANK kwa muda wa dakika 1

BOMBA C litajza 1/90 ya TANK kwa muda wa dakika 1

Mabomba yote matatu yatajaza (1/30) + (1/45) + (1/90) = 1/15 kwa muda wa dakika 1! (siyo dakika 3 tafadhali)

Kwa hiyo kama mabomba matatu yanaweza kujaza 1/15 ya TANK kwa muda wa dakika 1, then yana uwezo wa kujaza 15/15 ya TANK kwa muda wa dakika 1x15= dakika 15

Hivyo mabomba yote matatu yatajaza TANK hilo kwa muda wa dakika 15.

MUHIMU:
Hili swali limekaa katika mfumo wa applied/ business mathematics zaidi, yaani mahesabu ambayo yanatumiwa na watu katika shughuli za maisha za kila siku kama vile kwenye business. Na kama ni Chuo Kikuu, swali la mfumo wa namna hii anatkiwa aulizwe sana sana mtu anayesoma digrii kama vile ya Bachellor of Commerce au Engineering, na si mtu anayesoma let's say degree ya mahesabu perce. Hivyo unapofikia hatua ya kuli-solve kwa kutumia KDS na KKS (GCF and the like), unakuwa uko sahihi katika jibu, ila kwenye njia yako ya kufikia jawabu kidogo inakuwa ina mgogoro ukizingatia nature ya swali lenyewe.

Still, swali hili liko katika kiwango cha chini sana kuweza kuulizwa katika ngazi hizo nilizozitaja na nakumbuka kama wakati enzi hizo wakati sisi wazee tunasoma shule za msingi, maswali ya aina hii yalikuwa yanapatikana katika kitabu kimoja maarufu sana kilikuwa kinaenda kwa jina la: JIANDAE VEMA KUMALIZA ELIMU YA SHULE YA MSINGI, manuscript iliyokuwa popular sana enzi hizo kwa wanafunzi wa shule za msingi na tulikuwa tunakatiza kwa kuiita "JIANDAE". Ilikuwa ni enzi hizo miaka ya 1947 wakati tuku shule za msingi, enzi za mkoloni.

Si ndo sawa na maswali ya watu 5 walilima shamba la hekari 6 kwa siku 8, je watu 10 watalima shamba la hekari 4 kwa siku ngapi? Unakokotoa mpaka uwezo wa mtu mmoja kwa hekari moja halafu unarejea kwenye wingi ulioulizwa

 

[Kirchhoff]

Hii kitu nakumbuka tulifundishwa darasa la 5,ila ndo hivyo sikuzingatia maana hadi leo sijaonaga tenki yenye bomba 3 za kuingiza maji, ni kuchoshana tu.

i) assume there is a tank with three input pipes!

 

[Dojiny]

Another brain teaser: A water tank reservoir is connected to three water pipe supplies, pipes a, b and c. Pipe a alone can fill the tank in 30 minutes while pipe b can fill it in 45 minutes and pipe c alone can fill it in 90 minutes. How long will the reservoir tank fill up if all water pipes are opened to the tank at the same time.

3 Minutes

 

[doublep]

Let the first, second, third and fourth digit be v, x, y and z respectively...

Let's create the algebra..

V=X/2
X +Y=10 ---->Y=10-X
Z=X+1

SUM of all
V+X+Y+Z=23

Then it will be
X/2+X+10-X+X+1=23
X/2 +X +11=23
X/2+X =23-11=12(times by two each side)
3X =24
X =8

Then
V=X /2----->8/2=4
V=4

Then
X+Y =10 ---->Y =10-X ------>10-8=2
Y=2

Then
Z=X +1 ------>8+1=9
Z=9

So V, X, Y AND Z is 4,8,2,9 respectively

Hence we said that the above letter each represent the digit of the pin then the pincode will be 4829.

Solved.

Umenikumbusha mbali sn mkuu yaani kishule shule kabisa

 

[Kibishi]

Math Quiz

Here is a brain teaser: Quantitative Reasoning.

A house wife forgot her bank 'ATM PIN' which is a four digit number, but luckily she remembered some hints on how to recall this 'PIN'
Here are some of the clues
1) The 1st digit is half of the 2nd
2) The sum of the 2nd and 3rd is 10
3) The 4th is equal to the 2nd plus 1
4) The sum of all the digits is 23

What is the ATM PIN ?

Solution:
Let the first, second, third and fourth digits be a,b,c and d respectively.
a=(1/2)b .....(i)
b+c=10 .....(ii)
d=b+1 .....(iii)
a+(b+c)+d=23 .....(iv)
Substitute equation i, ii and iii into iv.
(1/2)b+10+b+1=23
(1/2)b+b=12
b+2b=24
3b=24
b=8.
From a=b/2 but b=8
a=4
From b+c=10 but b=8
c=2
From d=b+1 but b=8
d=9.
Hence the ATM PIN is 4829.

 

[Kibishi]

Another brain teaser: A water tank reservoir is connected to three water pipe supplies, pipes a, b and c. Pipe a alone can fill the tank in 30 minutes while pipe b can fill it in 45 minutes and pipe c alone can fill it in 90 minutes. How long will the reservoir tank fill up if all water pipes are opened to the tank at the same time.

Solution:
This is the 'inverse variation' case.
a¤1/30 =>a=k/30
b¤1/45 =>b=k/45
c¤1/90 =>c=k/90
Where k is constant and symbol ¤ is the 'proportional to' sign.
a+b+c=k/30+k/45+k/90=100%
k/30+k/45+k/90=1
Multiply by 90 both sides
3k+2k+k=90
6k=90
k=15
Hence, it will take 15 minutes the water tank reservoir to be filled by all water pipesa, b and c together.

 

[kuwese]

DECODED SERIES

 

[Qss]

Another brain teaser: A water tank reservoir is connected to three water pipe supplies, pipes a, b and c. Pipe a alone can fill the tank in 30 minutes while pipe b can fill it in 45 minutes and pipe c alone can fill it in 90 minutes. How long will the reservoir tank fill up if all water pipes are opened to the tank at the same time.

Let me try as follows;
Recall if pipe C alone can fill the tank in 90 min.and Pipe B alone can fill the tank in 45 min.and pipe A alone can fill the tank in 30 min.
Solution is 90-45-30=15
Therefore Water reservior tank will be filled in 15 minutes provided all pipes opened in the same time.

Hayo yote hayahitajiki katika hili swali, yangehitajika yangewekwa. Je unajua hili ni swali la o level siyo advance?.

 

[Makanyaga]

30 gramu/lita

Maswali ya rate huwa yanasumbua wakati mwingine.
Hebu tusaidie hili:

Tank la lita 50 limewekewa mchanganyiko wa maji na chumvi(soluble, kipimo/concentration ya 30 gramu/lita) kiasi cha lita 25 zimejazwa.
Kuna bomba limefunguliwa linaweka maji kwenye tank kiasi cha lita 3 kwa dakika na hapo hapo kuna mrija/tobo kwenye tank linachuruzisha maji kutoka kwenye tank kiasi cha lita 1¼ kwa dakika.

a) Tanki litajaa baada ya muda gani?
b) mchanganyiko wa kwenye tanki utasomaje wakati likijaa?

Kama nimeelewa swali lako, just from normal logic na si katika utaalamu wa mahesabu

Kuna lita 25 kwa kuanzia, na concentration ya 30g/l.

Kwa hiyo SOLUTE iliyo ndani ya mchanganyiko huo ni 25x30=750g

INFLOW rate ni 3 litres per minute na
OUTFLAW RATE ni 1¼=1.25 litres

Kwa hiyo TOTAL NET INFLOW ni 3-1¼=1.75 litres per minute

At a net inflow of 1.75 litres, (to make a total of 50 litres for the tank to be full) it will take 14.3 minutes for the tank to be full 25litre/1.75)

How many grams of the solute will be lost during this time interval of 14.3 minutes (i.e. The time taken for the Tank to be full at 50 litres)

Net inflow=1.75litres per minute

Original concentration 30g/litre

Time taken for the tank to be full at 50 litres=14.3 minutes

THEREFORE:

Total solute weight in the solution(at the time when the tank becomes full at 50 litres) =1.75litres per minutex30grams per litre x14.3 minutes (i.e 1.75x30x14.3)

Maswali ya rate huwa yanasumbua wakati mwingine.
Hebu tusaidie hili:

Tank la lita 50 limewekewa mchanganyiko wa maji na chumvi(soluble, kipimo/concentration ya 30 gramu/lita) kiasi cha lita 25 zimejazwa.
Kuna bomba limefunguliwa linaweka maji kwenye tank kiasi cha lita 3 kwa dakika na hapo hapo kuna mrija/tobo kwenye tank linachuruzisha maji kutoka kwenye tank kiasi cha lita 1¼ kwa dakika.

a) Tanki litajaa baada ya muda gani?
b) mchanganyiko wa kwenye tanki utasomaje wakati likijaa?

Hili swali lako ni very advanced na linaweza ku-involve a lot of calculus. However kulijibu kisahihi, knowledge is required either from calculus or chemistry or both. Will be back!

 

[shalet]

Naomba nijibu hili swali katika namna ambayo hata yule ambaye hajui hesabu atatelewa.

BOMBA A lina uwezo wa kujaza TANK kwa muda wa dakika 30. Kwa hiyo lina uwezo wa kujaza 1/30 ya tank kwa muda wa dakika 1, na kwa maana hiyo basi:

BOMBA A litajza 1/30 ya TANK kwa muda wa dakika 1


BOMBA B litajza 1/45 ya TANK kwa muda wa dakika 1

BOMBA C litajza 1/90 ya TANK kwa muda wa dakika 1

Mabomba yote matatu yatajaza (1/30) + (1/45) + (1/90) = 1/15 kwa muda wa dakika 1! (siyo dakika 3 tafadhali)

Kwa hiyo kama mabomba matatu yanaweza kujaza 1/15 ya TANK kwa muda wa dakika 1, then yana uwezo wa kujaza 15/15 ya TANK kwa muda wa dakika 1x15= dakika 15

Hivyo mabomba yote matatu yatajaza TANK hilo kwa muda wa dakika 15.

MUHIMU:
Hili swali limekaa katika mfumo wa applied/ business mathematics zaidi, yaani mahesabu ambayo yanatumiwa na watu katika shughuli za maisha za kila siku kama vile kwenye business. Na kama ni Chuo Kikuu, swali la mfumo wa namna hii anatkiwa aulizwe sana sana mtu anayesoma digrii kama vile ya Bachellor of Commerce au Engineering, na si mtu anayesoma let's say degree ya mahesabu perce. Hivyo unapofikia hatua ya kuli-solve kwa kutumia KDS na KKS (GCF and the like), unakuwa uko sahihi katika jibu, ila kwenye njia yako ya kufikia jawabu kidogo inakuwa ina mgogoro ukizingatia nature ya swali lenyewe.

Still, swali hili liko katika kiwango cha chini sana kuweza kuulizwa katika ngazi hizo nilizozitaja na nakumbuka kama wakati enzi hizo wakati sisi wazee tunasoma shule za msingi, maswali ya aina hii yalikuwa yanapatikana katika kitabu kimoja maarufu sana kilikuwa kinaenda kwa jina la: JIANDAE VEMA KUMALIZA ELIMU YA SHULE YA MSINGI, manuscript iliyokuwa popular sana enzi hizo kwa wanafunzi wa shule za msingi na tulikuwa tunakatiza kwa kuiita "JIANDAE". Ilikuwa ni enzi hizo miaka ya 1947 wakati tuku shule za msingi, enzi za mkoloni.

Kuna kitabu kiliindwa jipime chekundu kilikuwa na maswali hayo