SOLUTION: Can you show me the steps to solving this and how to set up an equation to solve it? Sarah and John are driving in opposite direction on a straight road. John is driving fifteen m

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Question 644568: Can you show me the steps to solving this and how to set up an equation to solve it?
Sarah and John are driving in opposite direction on a straight road. John is driving fifteen miles per hour faster than Sarah. After three hours they are 375 miles apart. How fast were Sarah and John traveling?
Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
With this type of problem, I like to think of
one of them standing still and the other one
moving at the sum of their speeds
Let Sarah's speed = mi/hr
John's speed = mi/hr
-----------
The equation of motion is

Sarah is traveling at 55 mi/hr
John is traveling at 70 mi/hr
check answer:
Sarah's distance =
mi
John's distance =
mi
as it should
OK

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Sarah and John are driving in opposite direction on a straight road. John is driving fifteen miles per hour faster than Sarah. After three hours they are 375 miles apart. How fast were Sarah and John traveling?
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You want to solve for "rate".
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Sarah DATA:
rate = x mph ; time = 3 hours ; distance = 3x miles
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John DATA:
rate = x+15 mph ; time = 3 hours ; distance = 3(x+15) miles
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Equation:
distance + distance = 375 miles
3x + 3(x+15) = 375
3x + 3x + 45 = 375
6x = 330
x = 55 mph (Sarah's rate)
x+15 = 70 mph (John's rate)
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Cheers,
Stan H.
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