Problema Solution
On a sales trip, Mark drives the 600 mi to Richmond averaging a certain speed. The return trip is made at an average speed that is 10 mph slower. Total time for the round trip is 22 hr. Find Mark’s average speed on each part of the trip.
Answer provided by our tutors
To Richmond DATA:
distance = 600 miles ; rate = x mph ; time = 600/x hrs
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From Richmond DATA:
distance = 600 miles ; rate = x-10 mph ; time = 600/(x-10) hrs.
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Equation:
time + time = 22 hrs
600/x + 600/(x-10) = 22
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600(x-10) + 600x = 22x(x-10)
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1200x - 6000 = 22x^2-220x
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22x^2 - 1420x + 6000 = 0
11x^2 - 710x + 3000 = 0
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Positive solution:
x = 60 mph (rate to Richmond)
x-10 = 50 mph (rate from Richmond)