Rational Expressions

Word Problem on Rates

A rate is an expression of the form a certain number of something per unit of time. One of the most common rates is mpg or miles per gallon. It expresses the number of miles a vehicle gets per 1 gallon of gas.

Example:

My car has a mileage rate of 22 mpg. How far can I get on 15 gallons of gas?

Multiplying the rate times the number of gallons of gas gives an answer of 22 x 15 = 330miles.

Example:

If a copy machine makes 30 copies per minute, its copy rate is 30 copies per minute.

If we then want to answer the question, how many copies can it make in 5 minutes, we multiply the rate of 30 copies per minute by 5 minutes to get 600 copies.

Notice the time units must be the same as those in the rate.

If we want to know how many copies can be made in 2 hours, we need to change 2 hours into 2 x 60 = 120 minutes, and then multiply 120 minutes by the rate of 30 copies per minutes to get 3600 copies.

How many copies can be made in 3 minutes and 40 seconds? We first need to change 40 seconds to a fraction of a minute by dividing 40 by 60 since there are 60 seconds in a minute.

    Thus, 40 seconds is two thirds of a minute.

Now we multiply 3 and two thirds minutes time the rate of 30 copies per minute. We need to change 3 and two thirds to an improper fraction.

Now multiplying gives

copies