Question

Amber and Austin were driving the same route from college to their home town. Amber left 2 hours before Austin. Amber drove at an average speed of 55 mph, and Austin averaged 75 mph per hour. After how many hours did Austin catch up with Amber?

Answer 1

Answer: 7.5 hours

Explanation:

Let x denote the number of hours taken by Amber was driving, then the time taken by Austin will be x-2 hours.

Since,
`\text{Distance=Speed*time}`

According to the question,

Distance traveled by Amber=
`55x`

Distance traveled by Austin=
`75(x-2)`

Also, when Austin caught up with Amber, their distances should be same.

i.e.
`75(x-2)=55x`

`75x-150=55x\\\\\Rightarrow\ 20x=150\\\\\Rightarrow\ x=7.5\text{ hours}`

Hence, after 7.5 hours Austin caught up with Amber.

Answer 2

7.5 hours

Explanation:

1 method:

Amber drove at an average speed of 55 mph.

Austin averaged 75 mph per hour.

The difference in speed is 20 mph, this means that each hour Austin drove 20 miles more.

Amber drove 110 miles in 2 hours, then Austin needs 110:2=5.5 hours to catch Amber, so in total after 5.5+2=7.5 hours Austin will catch up Amber.

2 method:

Let t hours be the time Amber was driving, then t-2 hours ia Austin's time.

Amber distance = 55t miles

Austin's distance = 75(t-2) miles

When Austin caught up with Amber, their distances are the same:

`55t=75(t-2)\\ \\55t=75t-150\\ \\75t-55t=150\\ \\20t=150\\ \\t=7.5\ hours.`