Time and Work #3

Question

Am confused by the question. Please explain the logic in solving this question.

To do a certain work C alone takes twice as long as A and B together; A would take 3 times as long as B and C together. All three together complete the work in 5 days. How long would each take separately?

Answer is 
A in 20, B in 12 and C in 15 days.

nammers · Answer

Could be too long winded as I am weaker at work rate problems but:

C alone takes twice as long as A and B together = 2AB
A and B together take 1 AB
The total time taken is 5 days so: 
2AB+1AB =5 days
1/rate = 1/3AB
1/1AB = (1/3AB) / 3
1/1AB = (1/5)* 1/3
1/1AB = 1/15
1AB = 15 days
as 1AB = C 
C takes 15 days

A:
3BC+BC = 5 days
1/rate = 1/4BC
1/1BC = (1/4BC) / 4
1/1 BC = (1/5) * 1/4
1BC = 20 days
A takes 20 days

B:
1/20+1/15+1/x = 1/5
1/20+1/15-1/5 = -(1/x)
3/60+4/60-12/60= -(5/60)
x=60/5 = 12 days

Could be done simpler, but made it longer so you know my process.

Hope this helps

cleetus · Answer

My Doubt is that the question says C= 2A+2B
So 2A+2B+A+B = 3(A+B) = Total Work = 1/5.
There for A+B = 1/5*1/3=1/15
So C = 1/5 -1/15 =2/15 or 7.5 days. But the answer is C did the work in 15 days.

Where did i go wrong

nammers · Answer

This is where the error occurs:

C= 2A+2B 
C actually works at half the rate, so is the equivalent of half of AB working alone, while A and B working together do the work at a rate of AB. So it is:
C=1/2(A+B)

1.5(A+B) = 1/5 <- this is the total time of A,B and C together
A+B = 1/5*2/3 = 2/15 <- the answer has now changed to show the rate of AB's work rate
A+B = 7.5 <- this is A and B working together
So double the rate becomes:
2*7.5 = 15 days

My first explanation did not make this inference clear.
Hope this is better

Spidy001 · Answer

1/A + 1/B = 1/(T1)---1

1/C = 1/(2T1)----2

1/A = 1/(3T2)----3

1/B + 1/C = 1/T2----4

1/A + 1/B + 1/C = 1/5---5

substituting 1 and 2 in 5 to find out T1

1/(T1) + 1/(2T1) = 1/5

=> T1 = 15/2

substituting 3 and 4 in 5 to find out T2

1/(3T2) + 1/(T2) = 1/5

=> T2 = 20/3

=> time taken by A = 3T2 = 20

time taken by C = 2T1 = 15

now we can use 1 or 4 to find out B's time = 12

cleetus · Answer

Thanks for the great help
Here is how i finally got it. This is easy infact and i made it look worse. My approach was wrong at first and that made my answer wrong.

C takes twice the time take by A and B together. 
So C takes half the the time of A+B. That is 
C = A+B/2 ; 2C = A+B
So adding one more C to the right and left we get 3C = A+B+C. A+B+C completes the work in 5 days.

So 3C = 1/5 and C = 1/5*3 = 1/15.
C alone take 15 days.

Now A alone take thrice the time by B and C together. Use the above strategy to find A's work rate and finally find B by adding A and C and subtracting it from total work i.e., 1/5

So A=20
 B = 12 and 
 C = 15
BINGO!!

Time and Work #3

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards