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.
