[GMAT math practice question]

There are 3 machines with the same work rate. If it took t hours for 3 machines to work and took t+2 hours for 2 machines when working together, what is the value of t?

A. 4
B. 5
C. 6
D. 7
E. 9
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The rate of work of each machine is the same.
Work done by 3 machines in 1 hr = \(\frac{1}{t}\)
Work done by 1 machine in 1 hr = \(\frac{1}{{3t}}\)
Work done by 2 machines in 1 hr = \(\frac{2}{{3t}}\) = \(\frac{1}{{t+2}}\)
\(\frac{2}{{3t}}\)=\(\frac{1}{{t+2}}\)
2t+4=3t
t=4

Answer A

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=>

Assume X is the time one machine takes to work.

1/T=3/X and 1/T+2=2/X

X = 3T and X = 2(T+2).
We have 3T = 2T + 4 or T = 4.

Thus, the answer is A.

Answer: A
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t/t+2=2/3
So, 3t=2t+4
=> t=4 hrs.
(A)