pushpitkc wrote:
Carter can finish a task in 20 hours, Lucas can finish the same task in 60 hours, and Lily can do so in 30 hours. Carter starts the work and is joined by Lucas after 10 hours. After another five hours, Carter leaves and Lily joins. How many hours will the task take to finish?
A. 2 hours and 40 minutes
B. 3 hours
C. 3 hours and 20 minutes
D. 18 hours and 20 minutes
E. 18 hours and 40 minutes
Source:
Experts GlobalCarter's rate :
\(\frac{1}{20}\)Lucas's rate :
\(\frac{1}{60}\)Lily's rate:
\(\frac{1}{30}\)Stage 1: Carter works for 10 hours. (Carter starts and "is joined by Lucas after 10 hours")
WORK finished:
\(r*t = W\)
W: \((\frac{1}{20}*10)=\frac{10}{20}=\frac{1}{2}W\) is finished
Work remaining: \(\frac{1}{2}W\)Time used: 10 hoursStage 2: Carter and Lucas work together for 5 hours
Combined work rate:
\((\frac{1}{20}+\frac{1}{60})=(\frac{3}{60}+\frac{1}{60})=\frac{4}{60}=\frac{1}{15}\)Work finished?
Together, C and L finish
W:
\((\frac{1}{15}*5)=\frac{1}{3}W\)Work remaining:
\((\frac{1}{2}W-\frac{1}{3}W)=\frac{1}{6}W\)Time used Stage 2: 5 hoursStage 3: Lily and Lucas finish the job (Carter leaves)
Combined rate, L and L:
\((\frac{1}{30}+\frac{1}{60})=(\frac{2}{60}+\frac{1}{60})=\frac{3}{60}=\frac{1}{20}\)L and L have
\(\frac{1}{6}W\) to finish
TIME they require to finish?
\(T=\frac{W}{r}\)
\(T=\frac{\frac{1}{6}}{\frac{1}{20}}=(\frac{1}{6}*\frac{20}{1})=\frac{20}{6}=\frac{10}{3}=3\frac{1}{3}\) hours
Total time taken to finish the work?
Stage 1 + Stage 2 + Stage 3 =
\(10 + 5 + 3\frac{1}{3}=
18\frac{1}{3}\) hours
Total time = 18 hours, 20 minutes
"How many hours will the task take to finish?"
I agree, this statement is ambiguous. I think, however, that if the writers had meant "time for Lily and Lucas to finish," the writers would have asked, "How many hours will the rest of the task take to finish?"
Answer D
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