Distance problem with unknown rate of speed

Question

A plane is traveling at a constant rate of speed from city A to city B and arrives in 2 hours. On the trip back from city B to city A the plane travels 10 miles per hour slower and arrives 30 minutes later. What is the distance in miles between city A and city B?

Answer 1

Let x = rate of speed from city A to city B

Let x-10 = rate of speed back from city B to city A

 

The distance is the same in both directions.

 

distance = speed * time

 

x * 2 hours = distance 

(x-10) * 2.5 hours = distance 

 

2x = 2.5x - 25

 

0 = 0.5x - 25

 

0.5x = 25

 

x = 50 miles per hour

 

distance = 50 mph *2 hours = 100 miles