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Question 112289: 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?
I started an equation but I'm not sure if it's right. 270/x and 330/x+10. I'm not sure where to go from here!
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Good start. But just to make sure you understand what is going on, let's go back to the basic
equation which relates distance, speed, and time. This equation is:
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D = S*T
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where D equals the distance, S represents the speed, and T is the time.
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If we substitute the values for Leon and let S represent Leon's speed then we get:
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270 = S * T
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So in Leon's case if we divide both sides of the equation by his speed, we get the amount of
time he drove as:
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T = 270/S
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Now let's do the same thing for Pat who went 330 miles at a speed of (S = 10). So Pat's
distance equation becomes:
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330 = (S+10)*T
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and solving for the time T that Pat drove (by dividing both sides by (S+10) we get:
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T = 330/(S+10)
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This is exactly what you got. So far, so good. Now all you have to do is to recognize that
the times that both Leon and Pat drove were the same. Therefore, Leon's time of 270/S equals
Pat's time of 330/(S+10). So we can set these two times equal:
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270/S = 330/(S+10)
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You can get rid of the (S+10) denominator by multiplying both sides of this equation
by (S+10) and the equation becomes:
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270(S+10)/S = 330
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Next you can get rid of the S denominator by multiplying both sides of the equation by S
to make the equation:
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270(S+10) = 330S
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Multiply out the left side:
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270S + 2700 = 330S
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Eliminate the 2700 on the left side by subtracting 2700 from both sides:
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270S = 330S - 2700
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and eliminate the 330s on the right side by subtracting 330S from both sides:
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-60S = - 2700
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Solve for S (which is Leon's speed) by dividing both sides of this equation by -60 to get:
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S = -2700/-60 = 45 mph
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So Leon drove at 45 mph and Pat, who drove 10 miles per hour faster, drove at 55 mph.
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Hope this helps you to see your way through the rest of the problem. You had an excellent start.
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