SOLUTION: A motorist completes a 450 mile journey in 8 hours. Before noon on this journey, he averages 60 mph, and after noon averages 50 mph. What time did he depart and what time did he ar

Question 237092: A motorist completes a 450 mile journey in 8 hours. Before noon on this journey, he averages 60 mph, and after noon averages 50 mph. What time did he depart and what time did he arrive?
i figured his avg time for the whole trip was 56.25 mph, so... im using d=rt formula, d=450; i know i don't add the 2 rates, 60 and 50 and solve for t. i tried and got 4.09, wrong. how do i go about solving ? help please-thanks
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A motorist completes a 450 mile journey in 8 hours. Before noon on this journey, he averages 60 mph, and after noon averages 50 mph. What time did he depart and what time did he arrive?
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Before noon DATA:
rate = 60 mph ; distance = x miles ; time = d/r = x/60 hrs
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After noon DATA:
rate = 50 mph ; distance = 450-x miles ; time = d/r = (450-x)/50 hrs
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Equation
time + time = 8 hrs
x/60 + (450-x)/50 = 8
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Multiply thru by 300 to get:
5x + 6(450-x) = 2400
5x + 6*450 - 6x = 2400
-x = -300
x = 300 miles (distance traveled before noon)
450-x = 150 miles (distance traveled after noon)
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Time before noon = x/60 = 300/60 = 5 hr.; He left at 7:00 AM
Time after noon = 150/50 = 3 hr. He arrived at 3:00 PM
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Cheers,
Stan H.
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