Question 108109: Paul and Charlene are 420 miles apart. They start toward each other with Paul driving 16 mi/h faster than Charlene. They meet in 5 hours. Find Charlene's speed.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let C be Charlene's rate
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Since Paul's rate is 16 mph more than C, then we can write that Paul's rate is C + 16.
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The distance each travels is their rate times the time that they drive at their rate. That
means that Charlene travels C*T miles. But T is given as 5 hours. Therefore, the distance that
Charlene travels in the 5 hours is 5*C. Meanwhile, Paul's rate times the time that he travels
at that rate is (C + 16)*T, and since T = 5 hours, the distance that Paul travels is 5*(C + 16).
This multiplies out to a distance of 5C + 80.
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The problem says that the total distance that is to be covered by the two drivers is
420 miles. In equation form, the sum of the distances covered by the two drivers is:
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5C + 5C + 80 = 420
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Add the two terms on the left side that contain C to get:
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10C + 80 = 420
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Get rid of the 80 on the left side by subtracting 80 from both sides to get:
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10C = 420 - 80 = 340
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Solve for C (Charlene's rate) by dividing both sides by 10 to get
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C = 340/10 = 34 mph
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You were asked to find Charlene's speed, and you have it .... 34 mph. [Paul's rate is 16
mph faster, so Paul drives at 50 mph.]
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Hope this helps you to understand the problem and to see how to find the solution.
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