It took Nina one hour longer to drive to her brother’s house than it did to return home. If it took Nina 6 hours to make the round trip and she traveled 20mph faster on the return trip, how fast did she drive on the way to her brother’s house?

Answer 1

If the distance is d, then since time = distance/speed,
d/s = d/(s+20) + 1
d/s + d/(s+20) = 6
s - 70 mi/hr on the way home
the distance is 175 miles

check:
175/50 = 3.5 hours to go
175/70 = 2.5 to return

Answer 2

How did you get 175 miles and 70mp/h

Answer 3

d/s = d/(s+20) + 1
d(s+20) = ds + s(s+20)
d(s+20)-ds = s(s+20)
d = s(s+20)/20

d/s + d/(s+20) = 6
d(s+20) + ds = 6s(s+20)
d(2s+20) = 6s(s+20)
d = 6s(s+20)/(2s+20)
Now eliminate d to get
s(s+20)/20 = 6s(s+20)/(2s+20)
1/20 = 6/(2s+20)
2s+20 = 120s = 50
Use that to get d=175