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uranmaximum [27]
3 years ago
14

Stephanie rode her new moped to Rod's house. Traveling the side streets, she avaraged 20 mph. To save time on the return trip, t

hey 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
Mathematics
1 answer:
Illusion [34]3 years ago
3 0

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.

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