Question

Amanda travels to work from home in 60

minutes. If, on her way home, she increases
her average speed by 20% and she travels
by the exact same route, how many
minutes will it take her to get home?

Answer 1

50 minutes

Step-by-step explanation:

We can set this up as a rate * time = distance problem. We can set the rate at which Amanda travels to work to be x, since that quantity is unknown. The time it takes is given to be 60 minutes. This means that the total distance she travels to get to work is 60x. On the other hand, the way back home has more unknown quantities. The exact rate is unknown, but we do know that it is 20% more than the rate at which Amanda travels to work. This means that the rate is x + .20x, or 1.2x. We can set the time to be y, which means the total distance she travels to get back home is 1.2xy. We are told that Amanda uses the same route to get to and from work, which means 60x = 1.2xy. All we have to do now is solve this equation:

`60x=1.2xy\\60=1.2y\\y=50`

If we divide through by x and then isolate y, we get that it takes Amanda 50 minutes to get home