Machines A and B, when working together at their constant rates, can produce 600 nails in z hours. If Machine A can produce 600 nails by itself in w hours, how long will it take Machine B to produce 600 nails alone?

Answer Choices

Correct answer marked below

z/(z+w)

w/(z+w)

zw/(z+w)

zw/(z-w)

zw/(w-z)

Correct

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Explanation

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Official Explanation

Official

When Machines A and B work together, they produce 600 nails in z hours.

Machine A, working alone, produces 600 nails in w hours.

We need to find out how long it takes Machine B to produce 600 nails by itself.

Let the rate of A be a and the rate of B be b. From the information given, we have a + b =

600/z

(1) and a =

600/w

(2). Substituting (2) into (1) gives us b =

600 (w-z) / zw

.…

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Comments

InaMay 16, 2024

thanksss

What this question tests

What it tests

Your ability to combine individual work rates, usually by working with the fraction of a job completed per unit of time.

Common trap

Adding the times instead of the rates, or forgetting to take the reciprocal when combining rates.