Question

Lucy can complete a sales route by herself in 9 hours. Working with an associate, she can complete a sales route in 5 hours. How long would it take her associate to do it working alone?

Answer 1

We know time and rate are inverses of each other.

Lucy's time is 9 hours. Hence, here rate will be:

$\frac{1}{9}$

Let Associate's time be 'a'.

Her rate is:

$\frac{1}{a}$

Together their time is 5 hours, so their rate will be 1/5

We can come up with the equation should below:

$\frac{1}{9}(5)+\frac{1}{a}(5)=1$

Let's solve for a:

$\begin{gathered} \frac{1}{9}(5)+\frac{1}{a}(5)=1 \\ \frac{5}{9}+\frac{5}{a}=1 \\ \frac{5}{a}=1-\frac{5}{9} \\ \frac{5}{a}=\frac{4}{9} \\ 4a=45 \\ a=\frac{45}{4} \\ a=11\frac{1}{4}\text{hours} \end{gathered}$

1/4th hour is

60/4 = 15 minutes

.

The time Lucy's associate takes to complete the sales route [working alone] is

11 hours 15 minutes