SOLUTION: How far can a person drive out into the country at the average of 40 mph and returen over the same road at the average of 30 mph if the total travel time (out and back) is 7 hours?

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Question 561284: How far can a person drive out into the country at the average of 40 mph and returen over the same road at the average of 30 mph if the total travel time (out and back) is 7 hours?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = distance into country in miles
Let +t+ = time to go into country in hrs
going in:
(1) +d+=+40t+
Coming back:
(2) +d+=+30%2A%28+7+-+t+%29+
-----------------
(2) +d+=+210+-+30t+
Substitute (1) into (2)
(2) +40t+=+210+-+30t+
(2) +70t+=+210+
(2) +t+=+3+
and, since
(1) +d+=+40t+
(1) +d+=+40%2A3+
(1) +d+=+120+ mi
The person can go 120 mi into country
check:
(2) +d+=+30%2A%28+7+-+t+%29+
(2) +120+=+30%2A%28+7+-+3+%29+
(2) +120+=+30%2A4+
(2) +120+=+120+
OK