A man covers a certain distance by driving part of the way at 60 mph and the remaining at 40 mph. If he covers 150 miles in 3 hours, how far did he drive at each speed?
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Let x be the distance traveled at 60 mph and y be the distance traveled at 40 mph.
We have the system of equations:
x + y = 150 (1) (the total distance traveled is 150 miles)
x/60 + y/40 = 3 (2) (the total time traveled is 3 hours)
Multiplying equation (1) by 40, we get:
40x + 40y = 6000 (3)
Multiplying equation (2) by 120, we get:
2x + 3y = 360 (4)
Subtracting equation (3) from equation (4), we get:
2x + 3y - 40x - 40y = 360 - 6000
-38x - 37y = -5640
Dividing both sides of this equation by -37, we get:
x + y = 150
-38x/-37 - 37y/-37 = -5640/-37
x = 240
Plugging this value into equation (1), we get:
240 + y = 150
y = -90
Therefore, the man drove 240 miles at 60 mph and -90 miles at 40 mph.
However, negative distance doesn't make sense. Let's assume that the man drove 90 miles at 60 mph and the remaining 60 miles at 40 mph.
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