Allison can complete a sales route by herself in 6 hours. Working with an associate, she completes the route in 4 hours. How long would it take her associate to complete the route by herself?

Question

please help

Answer 1

Allison completes a route in 6 hours. So she can do 1/6 route in 1 hour.

Her associate completes a route in a hours, so she does 1/a route in 1 hour.

Together their working speed is 1/6+1/a. But together it takes 4 hours to do a route so in an hour they can only do 1/4 of a route. Therefore 1/6+1/a=1/4.

Multiply through by 12a: 2a+12=3a, so a=12 hours, the time it takes the associate to complete a route alone.