Question

Stephanie rode her new moped to Rod's house. Traveling the side streets, she avaraged 20 mph. To save time on the return trip, they loaded the bike into Robs truck and took the freeway, averaging 50 mph. The freeway distance is 2 miles less than the distance on the side streets n save 24 minutes. Find the distance traveled on the return trip

Answer 1

Answer: the distance traveled on the return trip is 70 miles.

Step-by-step explanation:

Let d represent the distance travelled along the side streets.

Let t represent the time spent travelling along the side street

Traveling the side streets, she avaraged 20 mph.

Distance = speed × time

Therefore, distance travelled along the side streets is

d = 40t

On the return trip, Rob's truck took the freeway, averaging 50 mph. The freeway distance is 2 miles less than the distance on the side streets and they saved 24 minutes(24/60 = 0.4 hours). It means that the distance travelled on the return trip is (d - 2) miles and the time spent is

(t - 0.4) hours. Therefore

d - 2 = 50(t - 0.4)

d - 2 = 50t - 20 - - - - - - - - - - -1

Substituting d = 40t into equation 1, it becomes

40t - 2 = 50t - 20

50t - 40t = - 2 + 20

10t = 18

t = 18/10 = 1.8

d = 40t = 40 × 1.8

d = 72

The distance on the return trip is

72 - 2 = 70 miles.