Kristen must travel a toll road for a total of 120 miles. After 70 miles she realizes that she has traveled for one hour. How fast should should...

Kristen must keep her average speed at or below 65 mph.

In the first hour of her journey, she travelled 70 miles. This is too fast. If she continues at the same speed she will have to pay the $100 charge.

The total distance Kristen wishes to travel is 120 miles. So one hour into the journey, she has 50 miles remaining to travel (120-70=50).

We can calculate Kristen's average speed over the entire journey as follows, where V2 is her second speed.

((70 miles * 70 mph) + (50 miles * V2 mph))/120 = average speed

Kristen wants her average speed to stay under 65 mph. So we can solve for V2 as follows:

((120*65)-(70*70))/50=V2 = 58 mph

In order to avoid the charge, Kristen must finish her journey at 58 mph or slower.