SOLUTION: Mr. Smith traveled between two cities that were 750 km apart. On the return trip, he increased his average rate of travel by 20 kph and made the trip in 10 hours less time. Find hi

Question 532533: Mr. Smith traveled between two cities that were 750 km apart. On the return trip, he increased his average rate of travel by 20 kph and made the trip in 10 hours less time. Find his rate of travel in each direction.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Mr. Smith traveled between two cities that were 750 km apart. On the return trip, he increased his average rate of travel by 20 kph and made the trip in 10 hours less time. Find his rate of travel in each direction.
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Let s = his speed on the outbound trip
Then s + 20 = his speed on the return trip
Let t = his travel time on the outbound trip
Then t - 10 = his travel time for the return trip
Given: d = 750
Since distance = speed x time, for the two trips we have
750 = s*t
750 = (s+20)(t-10)
Solve for t in the 1st equation, substitute in the 2nd:
750 = (s+20)(750/s-10)
Solve for s:
750 = 750 - 10s + 15000/s - 200
Simplify:
s^2 + 20s - 1500 = 0
Factor:
(s+50)(s-30) = 0
Take the positive solution, s = 30
So the rates are 30 kph and 50 kph
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