Algebra Word Problem

Question

A car and a motorcycle leave at noon from the same location, heading in the same direction. The average speed of the car is 30 mph slower than twice the speed of the motorcycle. In two hours, the car is 20 miles ahead of the motorcycle. Find the speed of both the car and the motorcycle, in miles per hour.

 

Car Speed:

 

Motorcycle Speed: 

Answer 1

Let  C = average speed of car (mph)

      M = average speed of motorcycle (mph)

      t = 2 hrs

 

Distance = speed x time

 

1) C = 2*M - 30

 

2)  D = (C - M)*t

    20 = (C - M)*2

 

Inserting equation 1) into equation 2) and solving for M:

 

20 = [(2*M -30) - M]*2       (divide all terms by 2)

 

10 = (2*M - 30) - M

 

10 = M - 30

 

M = 10 + 30 = 40 mph (speed of motorcycle)

 

C = 2*M - 30 = 2*(40) - 30 = 80 - 30 = 50 mph (speed of car)