SOLUTION: Hi, I need help with this word problem please! A motorist drove 150 miles on the country road before driving 50 miles on the mountain road. The rate of speed on the country roads

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Question 123681: Hi, I need help with this word problem please!
A motorist drove 150 miles on the country road before driving 50 miles on the mountain road. The rate of speed on the country roads was 3 times the rate on the mountain roads. The time spent traveling the 200 miles was 5 hours. Find the rate of the motorist on the country road.
THANK YOU!
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A motorist drove 150 miles on the country road before driving 50 miles on the mountain road. The rate of speed on the country roads was 3 times the rate on the mountain roads. The time spent traveling the 200 miles was 5 hours. Find the rate of the motorist on the country road.
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Country road DATA:
Distance = 150 miles ; rate = 3x mph ; time = 150/3x = 50/x hrs.
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Mountainroad DATA:
Distance = 50 miles ; rate = x mph ; time = 50/x hrs
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EQUATION:
time + time = 5 hrs
50/x + 50/x = 5
100/x = 5
Invert to get:
x/100 = 1/5
x = 20 mph (rate on the mountain road)
3x = 60 mph (rate on the country road)
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Cheers,
Stan H.