a motorist drove 150 miles on country roads before driving 5

a motorist drove 150 miles on country roads before driving 50 miles on mountain roads. the rate of speed on the country roads was 3 times the rate on mountain roads. the time spent traveling the 200 miles was 5 hours. find the rate of the motorist on country roads?
i let x=rate of the motorist on mountain road
and 3x rate of the motirist on country roads
i set up the equation x/200 - 3x/200 = 5

Solution

Country Road DATA:
distance = 150 miles ; rate = 3x mph ; time = d/r = 150/(3x) = 50/x hrs.
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Mountain Road DATA:
distance = 50 miles ; rate = x mph ; time = d/r = 50/x hrs
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Equation:
time + time = 5 hrs
2(50/x) = 5
100/x = 5
5x = 100
x = 20 mph on mountain Roads
3x = 60 mph on country Roads