SOLUTION: Leon drove 270 miles to the lodge in the same time as Pat drove 330 miles to the lodge. If Pat drove 10 miles per hour faster than Leon, then how fast did each of them drive?

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Question 7153: Leon drove 270 miles to the lodge in the same time as Pat drove 330 miles to the lodge. If Pat drove 10 miles per hour faster than Leon, then how fast did each of them drive?
Answer by glabow(165) About Me  (Show Source):
You can put this solution on YOUR website!
Since the time taken to make a trip is distance / speed we can calculate
time = 270 / LeonSpeed = 330 / PatSpeed. We also know that PatSpeed = LeonSpeed + 10. Putting that into the equation, we have
270%2FLeonSpeed+=+330%2F%28LeonSpeed%2B10%29
We solve for LeonSpeed.
270+%28LeonSpeed%2B10%29+=+330+%28LeonSpeed%29
270+LeonSpeed+%2B+2700+=+330+LeonSpeed
2700+=+60+LeonSpeed
So, LeonSpeed+=+45 and PatSpeed+=+55
Checking 220/45 = 330/55 = 6.