Question 115248: Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 108 miles in the same time that Dana travels 99 miles. If Chuck's rate of travel is 3 mph more than Dana's, and they travel the same length of time, at what speed does Chuck travel?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Use the formula that Distance equals Speed times Time to solve this equation. In equation
form this is:
.
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For Chuck, the distance he traveled was 108 miles. His speed was  where the "c" indicates
it is Chuck's speed. Substituting these into the equation for chuck results in:
.
.
Solve this equation for T by dividing both sides by to get:
.
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Meanwhile, Dana travels 99 miles in the same time. Let  represent Dana's speed.
Substituting these values into the distance equation results in:
.
.
Solve this equation for T by dividing both sides by and it becomes:
.
.
So we have two equations for T ... one for Chuck and one for Dana. But, according
to the problem, both drivers drive for equal times. So the two T equations are equal. That
means the right sides of these equations are equal for the two drivers. So it can be said
that:
.
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Next the problem tells you that Chuck's speed is 3 miles per hour more than Dana's. So
it also can be said that:
.
.
Substitute the right side of this into the Time equation and the result is:
.
.
Put both of these fractions over a common denominator by multiplying both sides of this
equation by  . Note that since the numerator of this
multiplier is equal to the denominator, this is equivalent to multiplying both sides of the
equation by 1.
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This multiplication leads to:
.
.
Cancel the like terms in the denominators and numerators on both sides:
.
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This leaves:
.
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Since the denominators are the same on both sides, the numerators must be equal. So, setting
the numerators equal results in:
.
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Multiplying out the right side results in:
.
.
Subtract  from both sides to get rid of that term on the right side and the
result is:
.
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Solve for by dividing both sides by 9 to get:
.
.
So Dana's speed is 33 miles per hour. And Chuck's speed, which is 3 miles per hour faster,
is 36 miles per hour.
.
Check. At 36 miles per hour it will take Chuck 3 hours to go 108 miles. And at 33 miles per
hour, it will take Dana 3 hours to go 99 miles. The answer checks because the times are equal.
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Hope this helps you to understand the problem and to see how it might be solved.
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