A truck enters a freeway traveling 40 mph. One hour later a car enters the same freeway traveling 55 mph...?

Let t = time required
40(t + 1) = 55t
40g + 40 = 55t
40 = 15t
8/3 = t

55(8/3) = 440/3 = 146.6666... ≈ 146.67 mi

Let T be the amount of time in hours it will take for the car to catch up to the truck. Using the fact that speed*time= distance, the following equation can be formed

40(T+1)=55T=>T=8/3.

This means that it will take the car 8/3 hours to catch up, or 55*8/3=440/3 more miles.

55 * (40 / (55 - 40))
= 55 * 40 / 15
= 11 * 40 / 3
= 440 / 3
= 146 2/3

*Explanation of formula
The initial distance between car and truck is 40 miles because the truck has traveled for one hour when the car starts to catch up.

The car can shorten the distance by 55 - 40 miles in an hour since it is runing at 55 mph while truck at 40 mph.

Total time to catch-up
= distance / catch-up speed
= 40 / (55 - 40)

Total distance traveled for catch-up
= car speed * catch-up time
= 55 * 40 / (55 - 40)

The first truck already has a 40mph*1hr = 40 mile head start. After t more hours, it will have gone another 40t miles, for a total of 40 + 40t miles. In that same time, the second truck will have gone 55t miles. We want to find the value of t when the two distances are equal to each other, so:
40 + 40t = 55t

Once we find t, we can use that to find the total number of miles, 55t.

40t+40=55t
40=15t
t=8/3 hours

55t=x
55(8/3)=146.67 mi