Work Rate Problem

GRE Quant Problem Solving
1

Machine A can do a job 50% faster than machine B. When they work together, they can complete a job in 4 hours. Approximately, how long does it take Machine A to complete the job alone?

I read on gmatclub that : ratio of time taken will be inverse of the ratio of rate of work since work done in both the cases is the same

So here :
rA /rB = 1.5/1 = 3/2
Time would be inverse so: tA/tB = 2/3
tA/(tA+tB) = 2/5
2/5 = tA/4
so tA=8/5 hours but the answer is 20/3 hours. Could someone explain where I went wrong? Did I misunderstand the inversion rule b/w rate and time?

2

tA + tB is not the same as t(A+B)
You can add rates when machines work together, not time
Imagine if a printer prints 10 pages per minute
If we use two printers we will have 20 pages per minute
The time taken to print has reduced not increased

Coming back to the problem:
rA/rB = 3/2
rB = 2 rA/3
r(A+B) = 1/t(A+B) = 1/4
r(A+B) = r(A) + r(B) = 1/4
r(A) + 2 rA/3 = 1/4
5 rA/3 = 1/4
rA = 3/20
tA = 1/rA = 20/3

3

Ohhh yeah you are right! You can only add the rates. THANK YOU! :slight_smile: