Givens
Slower car
r = r
t = 12 hours
d = ?
Faster car
r = r + 20
t = 8 hours
d = ?
It doesn't matter what the exact distance is. You just have to know that the 2 distances are equal ie going to the mountains from his home is the same distance as going from the mountains to his home.
d = r * t
r * 12 hours = (r + 20)* 8 hours. Remove the brackets on the right
r*12 = 8r + 20*8
r*12 = 8*r + 160
r*12 - 8r = 8r - 8r + 160
4r = 160
r = 40 miles / hour
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Slower Ride determines the distance.
d = r*t
d = 40 * 12
d = 480
Check
Use the faster rate (r + 20) = 40 + 20 = 60 mph
60 * 8 = 480. Both distances work out to be the same.