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:

`(1)/(9)`

Let Associate's time be 'a'.

Her rate is:

`(1)/(a)`

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

We can come up with the equation should below:

`(1)/(9)(5)+(1)/(a)(5)=1`

Let's solve for a:

`\begin{gathered} (1)/(9)(5)+(1)/(a)(5)=1 \\ (5)/(9)+(5)/(a)=1 \\ (5)/(a)=1-(5)/(9) \\ (5)/(a)=(4)/(9) \\ 4a=45 \\ a=(45)/(4) \\ a=11(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