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A
rate is a ratio that compares
two different kinds of numbers, such as miles per hour,
or inches per minute. A unit
rate compares a quantity to its unit of measure. |
A rate expresses how long
it takes to do something.
To drive 50 inches in one minute is to drive at the rate of 50 in./min.
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The fraction expressing a rate
has units of distance in the numerator and units of time in the
denominator. |
Solving a problem dealing with rate
usually involves solving a proportion.
Examples:
1.
How long, in minutes, did it take the
bug to cover 350 inches at a rate of 50 inches per minute?
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Use "cross multiply" (in a proportion, the
product of the means equals the product of the extremes) to
solve. |
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Answer: 7 minutes |
2.
The bug drives his
matchbox cruiser to his friends house traveling at the rate of 50
inches per minute. He then walks back to his home at the rate
of 10 inches per minute. If the round trip took 9 minutes, how
far is it from the bug's home to his friend's house?
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Distance = Distance
Let t = time
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Distance =
Rate x Time
The distance driving the cruiser to the friend's house
is the same distance that the bug walks back home = round
trip.
Hint: We need to first find the time which
can then be used to find the distance. |
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Answer: Distance =
50t = 50(1.5) = 75 inches
Also 10(9 - t) = 10(9 - 1.5) = 10(7.5) = 75 inches |
