SOLUTION: A family drove to a resort at an average speed of 30 mph and later returned over the same road at an average speed of 50 mph. Find the distance to the resort if the total driving t

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Question 97397This question is from textbook Algebra Beginning and Intermediate
: A family drove to a resort at an average speed of 30 mph and later returned over the same road at an average speed of 50 mph. Find the distance to the resort if the total driving time was 8 hours. This question is from textbook Algebra Beginning and Intermediate

Answer by longjonsilver(2297) (Show Source):
You can put this solution on YOUR website!
speed=distance/time.

let distance=d
let t = time going
let T = time returning

going: 30 = d/t --> t = d/30
returning: 50 = d/T --> T = d/50

so t+T = d/30 + d/50

but we are told that the total time of the trip (ie t+T) is 8hours, so we have 8 = d/30 + d/50

so we have a fractional equation to solve. If we multiply every term by 150, we get
and now we can cancel the fractions, leaving

1200 = 8d
d = 1200/8
d = 150miles

cheers
Jon.