Here is a Tip on work/rate problems. I would like to introduce Percent approach to solve Work/rate problems.
Let's consider basic example.
A can complete a certain task in 10 hours and B can complete the same task 20 hours.
We assume that the task is 100%
So if A can complete the task in 10 hours, we can say he is taking 10 hours to complete 100% of task. That means in one hour he is finishing \(\frac{100%}{10}\) or 10% task.
Similarly B is completing \(\frac{100%}{20}\) or 5% task in one hour.
If they start working together(at their respective rates), they would finish (10% + 5%) or 15% task in one hour.
So to finish entire task together, it would take them \(\frac{100}{15}\) or \(6\frac{2}{3}\) hours.Now lets apply this logic on following GMAT Type question. This is question is taken from
Bunuel's Set of Mixed questions.Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C together complete the task in 15 minutes. What is the value of x?
A. 1
B. 1.25
C. 2
D. 2.5
E. 4
Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours respectively
So in one hour A is completing 10% task, B is completing 20% task, and C is completing \((\frac{100}{x})%\) task.A starts working alone and 2 hours later B joins.
Before B joins, A will have worked for 2 hours and have finished 20% task. That means when B joins A, total remaining work will be 80%After another 2 hours joins C.
Using Similar logic, At the time of C's joining, A & B will have finished 60% task. Remaining work will be 20% After that A, B, and C together complete the task in 15 minutes.
So A, B, C together complete remaining 20% task in 15 mins or in \(\frac{15}{60} hours\)So we have that \(\frac{20%}{(10% + 20% + 100/x)} = \frac{15}{60}\)Solving for X, we get 750x = 1500 ----------> x = 2Hope that helps!!
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