Distance problems

Question

A car and a truck are leaving a city traveling in opposite directions. The car is going 12 mph slower than the truck. After 3/4 hours, the car reaches its destination. After 2 1/2 hours the truck reaches its destination. They end up 199 miles apart. Find the speed of each vehicle

Answer 1

We know that the total distance traveled by the vehicles is 199 miles since that's how far apart they end up.

 

If we say r = the speed of the truck then the distance traveled by the truck is 2.5r

 

Since the car is going 12 miles per hour slower, the rate of the car is r - 12.  The distance traveled by the car is 3/4(r-12)

 

The total distance traveled by both vehicles is 3/4(r-12) + 2.5r and that equals 199

 

So:

3/4(r-12) + 2.5r = 199

 

Now you can solve for r and find the truck's speed from there.