A motorist completes a 450 mile journey in 8 hours Before no

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

Solution

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