Question

How many hours will it take Ann and Peter, working together at their respective constant rates, to make 100 copies of a certain document? (1) It takes two hours for Ralph to make 100 copies by himself. (2) It takes 75 minutes for Ann, Peter, and Ralph working together to make 100 copies.

Answer 1

Answer:

Peter and Ann will make 100 copies together in 3.33 hours.

Step-by-step explanation:

Let Ann took the time to make 100 copies of a certain document = x hours

Then per hour work done by Ann = $\frac{1}{x}$

Time taken by Ralph to compete the work = 2 hours

So per work done by Ralph = $\frac{1}{2}$

Let the time taken by Peter to complete the work = y hours

Per hour work done by Peter = $\frac{1}{y}$

It took 75 minutes or $\frac{75}{60}$ hours by Ann, peter and Ralph together to complete the task.

Then per hour work done by all = $\frac{60}{75}$

And the equation representing per hour work done will be,

$\frac{1}{x}+\frac{1}{y}+\frac{1}{2}=\frac{60}{75}$

$\frac{1}{x}+\frac{1}{y}+\frac{1}{2}=\frac{4}{5}$

$\frac{1}{x}+\frac{1}{y}=\frac{4}{5}-\frac{1}{2}$

$\frac{1}{x}+\frac{1}{y}=\frac{8-5}{10}$

$\frac{1}{x}+\frac{1}{y}=\frac{3}{10}$

Since per hour work done by Ann and Peter is $\frac{3}{10}$

So time taken to complete the same work by both together will be $\frac{10}{3}$ or 3.33 hours.