Question 117047: A bicyclist rode into the country for 5 hr. In returning, her speed was 5 mi/h faster and the trip took 4 hr. What was her speed each way? Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! Use the equation:
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for the two parts of this problem. D represents the distance traveled, R the rate or speed
of the travel, and T the time spent traveling.
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For the first part of the problem, call the unknown rate of travel S (standing for speed). And the
problem tells you that the bicyclist rode out into the country for a time T equal to 5 hours.
Putting these values into the Distance equation results in:
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On the return trip the Rate is S + 5 because you are told that it is 5 miles per hour faster
than on the ride out into the country. You are also told that the duration of the return
ride is 4 hours. Putting these values into the Distance equation for the return ride results in:
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Do the distributed multiplication on the right side by multiplying the 4 times each of the
two terms in the parentheses. This multiplication results in the Distance equation becoming:
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Now recognize that the two distances ... the one going into the country and the one returning
are equal. So the right sides of the two Distance equations must be equal. In equation form
this is represented as:
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Get rid of the 4S on the right side by subtracting 4S from both sides. Subtracting 4S
from both sides reduces the equation to:
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This tells us that the bicyclist rode at a speed of 20 miles per hour going out into the country,
and, since the rate or speed was 5 miles per hour faster on the return trip, the speed on
the return trip was 25 miles per hour.
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And as add information (not required by the problem) the distance she rode into the country
can be determined by multiplying her speed of 20 miles per hour on the outbound trip by the 5 hours
she spent on this portion of the trip. 20 times 5 is 100 miles. On the return trip she rode
at a speed of 25 miles per hour for hours, and 25 times 4 also equals 100 miles, just as it is
supposed to since the distances are equal in both directions.
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Hope this helps you to understand the problem a little better and helps you to understand the
equation that says Distance equals Rate times Time.
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