SOLUTION: A driver took a​ day-trip driving at two different speeds. He drove 50 miles at a slower speed and 140 miles at a speed 10 miles per hour faster. If the time spent during the fas

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Question 1155290: A driver took a​ day-trip driving at two different speeds. He drove 50 miles at a slower speed and 140 miles at a speed 10 miles per hour faster. If the time spent during the faster speed was twice that spent at a slower​ speed, find the two speeds during the trip.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


time = distance / rate

x = lower speed
x+10 = higher speed

time to go 50 miles at lower speed: 50/x
time to go 140 miles at higher speed: 140/(x+10)

The time at the higher speed is twice the time at the lower speed:

140%2F%28x%2B10%29+=+2%2A%2850%2Fx%29

140%2F%28x%2B10%29+=+100%2Fx

100x%2B1000+=+140x

1000+=+40x

x+=+25

The two speeds are 25mph and 35mph.

CHECK:
50 miles at 25mph = 2 hours
140 miles at 35mph = 4 hours