Please help me solve this problem. I have tried, but it seems like something is missing. Rosa drives to Barnesville at 50 mph and returns by a road 5 miles longer at 40 mph. The return trip takes 15 minutes longer. How long is each road? Solution Distance = (rate in mph)(time in hrs.) Data going to Barnesville: Let distance = d; rate is 50mph; time is t Data returning: distance = d+5; rate is 40mph; time is (t+(1/4) Equations To Barnesville: d = 50t From Barnesville: d+5 =40(t+(1/4)) Solve by substitution: 50t + 5 = 40t+10 10t = 5 t = 1/2 Solve for distance: To Barnes: d = 50t = 50(1/2) = 25 miles From Barnes: d+5 = 20 miles.

1. Please help me solve this problem. I have tried, but it seems like something is missing.
Rosa drives to Barnesville at 50 mph and returns by a road 5 miles longer at 40 mph. The return
trip takes 15 minutes longer. How long is each road?
Solution
Distance = (rate in mph)(time in hrs.)
Data going to Barnesville:
Let distance = d; rate is 50mph; time is t
Data returning:
distance = d+5; rate is 40mph; time is (t+(1/4)
Equations
To Barnesville: d = 50t
From Barnesville: d+5 =40(t+(1/4))
Solve by substitution:
50t + 5 = 40t+10
10t = 5
t = 1/2
Solve for distance:
To Barnes: d = 50t = 50(1/2) = 25 miles
From Barnes: d+5 = 20 miles