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Andy and Ben can finish painting a wall in x hours working together.
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22 Dec 2024, 22:44
22 Dec 2024, 22:44
Expert Reply
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Question Stats:
38% (02:47) correct
61% (02:13) wrong based on 26 sessions
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Andy and Ben can finish painting a wall in x hours working together. Andy takes y hours more than Ben to finish the same work when both of them work alone.
Quantity A |
Quantity B |
Number of hours that Ben takes to finish the same work alone |
\(\frac{x-y}{2} \) |
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Re: Andy and Ben can finish painting a wall in x hours working together.
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30 Dec 2024, 01:02
30 Dec 2024, 01:02
Can you explain a bit?
Re: Andy and Ben can finish painting a wall in x hours working together.
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30 Dec 2024, 01:36
30 Dec 2024, 01:36
1
Expert Reply
Let the speed at which Andy and Ben do the work is A units/hour \& B units/hour respectively.
So, the time taken by Andy and Bob to finish the work would be $\(\frac{1}{\mathrm{~A\)$ hours \& $\(\frac{1}{\mathrm{~B\)$ hours respectively. ( $\(\because\)$ Speed \& Time are inversely proportional when Work is constant)
As we know that Andy and Ben together finish the work in ' $\(x\)$ ' houirs, so their combined speeds is $\(\frac{1}{x}\)$, we get $\(A+B=\frac{1}{x} \ldots\)$ (1) Also it is given that the time taken by Andy to finish the work alone is ' $\(y\)$ ' hours more than the time taken by Ben alone to finish the work, so we get $\(\frac{1}{A}-\frac{1}{B}=y \ldots . .(2)\)$
Subtracting equations (1) \& (2) we get $\(\frac{2}{B}=x-y \Rightarrow \frac{1}{B}=\frac{x-y}{2}\)$ which is equal to the time that Ben would take to finish the work alone.
Hence column (A) has same quantity as column (B), so the answer is (A).
So, the time taken by Andy and Bob to finish the work would be $\(\frac{1}{\mathrm{~A\)$ hours \& $\(\frac{1}{\mathrm{~B\)$ hours respectively. ( $\(\because\)$ Speed \& Time are inversely proportional when Work is constant)
As we know that Andy and Ben together finish the work in ' $\(x\)$ ' houirs, so their combined speeds is $\(\frac{1}{x}\)$, we get $\(A+B=\frac{1}{x} \ldots\)$ (1) Also it is given that the time taken by Andy to finish the work alone is ' $\(y\)$ ' hours more than the time taken by Ben alone to finish the work, so we get $\(\frac{1}{A}-\frac{1}{B}=y \ldots . .(2)\)$
Subtracting equations (1) \& (2) we get $\(\frac{2}{B}=x-y \Rightarrow \frac{1}{B}=\frac{x-y}{2}\)$ which is equal to the time that Ben would take to finish the work alone.
Hence column (A) has same quantity as column (B), so the answer is (A).
