RTCNTC said:A can do a piece of work in 25 days and B can do the same work in 30 days. They work together for 5 days and then A leaves. B will finish the remaining work in...
a) 21 days
b) 11 days
c) 20 days
d) 19 days
Is the following equation correct?
1/25 + 1/B = 1/5
RTCNTC said:I don't follow the logic.
MarkFL said:In order to answer this question, we need to know how long it takes A and B working together to complete one task, because we need to know how much of the task will be remaining after 5 days. We'll call this length of time T. Instead of the method I presented, we could also write:
\(\displaystyle \frac{1}{25}+\frac{1}{30}=\frac{1}{T}\)
This equation arises from looking at what gets done in 1 unit of time (days in this problem). In 1 day, A can complete 1/25 of a task and B can complete 1/30 of a task, and so the LHS of the equation represents their combined effort in 1 day. Since we've defined T to be the amount of time it takes A and B to complete a task working together, their combined efforts for 1 day, must equal 1/T.
What do you get when you solve for T?
RTCNTC said:I got T = 150/11.
RTCNTC said:I got 19/30.
RTCNTC said:(19/30)(30) = 19 days
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