Precalculus word problem

Question

truck enters a highway driving 60 mph. A car enters the highway at the same place

13

minutes later and drives

75 mph in the same direction. From the time the car enters the​ highway, how long will it take the car to pass the​ truck? Round to the nearest minute

Answer 1

Lets draw a picture of this:

Since we are given speed in miles/hour and time in minutes, we will need to convert to the same units of measure. So lets put speed into miles per minute. 60miles/hr x 1hr/60min = 1 mile/min. 75 miles/hr x 1hr/60min = 1.25 miles/min.

Since distance = speed*time, looking at Time 1, the distance the truck went was 1 mile/min x 13 min = 13 miles.Looking at Time 2, he went an additional distance of 1mi/min*t. His total distance was 13 + 1*t or 13 + t.

The car traveled a total distance of 1.25*t or 1.25t. The distance the car traveled and the distance the truck traveled are the same at the point when the car is passing the truck so 13 + t = 1.25t. Now solve for t.

13 + t = 1.25t.

13 = 0.25t

t = 13(4) = 52 min

Checking:

After 52 minutes, the truck traveled 52 miles (going 1 mile/min) plus the 13 miles he had gone before the car started or 65 miles. After 52 minutes, the car traveled 52*1.25 = 65 miles

Answer 2

The truck is going 60 miles per hour. Since there are 60 minutes in one hour, the truck is going one mile per minute. In 13 minutes the truck is therefore 13 miles ahead of the car when the car enters the highway. The car is going 75 miles per hour and the truck is going 60 miles per hour, so the difference in speeds is

75-60 = 15 miles per hour.

You can think of the problem in the following terms - if we subtract 60 miles per hour from the speed of each vehicle, the truck is stopped (13 miles ahead) and the car is going 15 miles per hour.

Now, the problem becomes, how long does it take the car to travel 13 miles going at a speed of 15 miles per hour?

13/15 = 0.866666 hours. Multiplying this by 60 minutes/hour gives the final answer of 52 minutes.