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. what's the speed of the car and motorcycle?

Answer 1

Explanation:

Formula

d = r * t

d is the distance

r = the speed

t = the time travelled.

Givens

Motorcycle

d = y

r = x

t = 2 hours

Car

d = y + 20

r = 2x - 30

t = 2 hours

Solution

Motorcycle

y = x*2

Car

y + 20 = (2x - 30)*2

Substitute y = 2x in the car. The rate of the motorcycle is the base rate.

2x + 20 = (2x - 30)*2 Remove the brackets

2x + 20 = 4x - 60 Subtract 2x from both sides

20 = 4x - 2x - 60 Combine

20 = 2x - 60 Add 60 to both sides

20+60 = 2x Combine

80 = 2x Divide by 2

80/2 = 2x/2

x = 40 miles per hour

Check

Distance motorcycle travels in 2 hours is 40 * 2 = 80 miles

Distance car travels in two hours is 2(2*40 - 30)

Distance car travels in two hours is 2*(80 - 30)

Distance car travels in two hours is 2* 50 = 100 miles

100 miles is 20 miles more than 80. The answer must be correct.

Answer

Speed motorcycle is 40 mph

Speed Car = 2 * 40 - 30 = 80 - 30 = 50 miles per hour