Question

Justin recently drove to visit his parents who live 270

miles away. On his way there his average speed was 11 miles per hour faster than on his way home (he ran into some bad weather). If Justin spent a total of 9 hours driving, find the two rates.

Answer 1

• 66 mph to visit
• 55 mph to home

Explanation:

An equation can be set up and solved based on the relation between the two speeds and the relation between time, speed, and distance.

Setup

time = distance/speed

Let x represent the (slower) speed on the way home. Then the total time for the round trip was ...

time going + time coming home = total time

270/(x +11) +270/x = 9

Solution

30x +30(x +11) = x(x +11) . . . . . . multiply by x(x+11)/9

x^2 -49x -330 = 0 . . . . . . . . rewrite in standard form

(x -55)(x +6) = 0 . . . . . . . . factor

x = 55 or x = -6 . . . . . . . solutions to this equation; x < 0 is extraneous

Justin's rate on the way there was 66 mph; on the way home, it was 55 mph.