- Time: x hours cycling
- Rate: 100 miles per hour
- Distance: 480 miles
So it takes the cyclist 4.8 hours to finish the race.
Work
In work questions, you will usually find the first quantity measured in time, the second quantity measured in work done, and the rate measured in work done per time. For example, if you knitted for 8 hours and produced two sweaters per hour, then:
Here is a sample work problem. It is one of the harder rate questions you might come across on the Math IC:
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Four men can dig a 40 foot well in 4 days. How long would it take for 8 men to dig a 60 foot well? Assume that these 8 men work at the same pace as the 4 men. | |
First, let’s examine what that problem says: 4 men can dig a 40 foot well in 4 days. We are given a quantity of work of 40 feet and a time of 4 days. We need to create our own rate, using whichever units might be most convenient, to carry over to the 8-men problem. The group of 4 men dig 40 feet in 3 days. Dividing 40 feet by 4 days, you find that the group of 4 digs at a pace of 10 feet per day.
From the question, we know that 8 men dig a 60 foot well. The work done by the 8 men is 60 feet, and they work at a rate of 10 feet per day per 4 men. Can we use this to answer the question? Yes. The rate of 10 feet per day per 4 men converts to 20 feet per day per 8 men, which is the size of the new crew. Now we use the rate formula:
- Time: x days of work
- Rate: 20 feet per day per eight men
- Total Quantity: 60 feet
This last problem required a little bit of creativity—but nothing you can’t handle. Just remember the classic rate formula and use it wisely.
Price
In rate questions dealing with price, you will usually find the first quantity measured in numbers of items, the second measured in price, and the rate in price per item. Let’s say you had 8 basketballs, and you knew that each basketball cost $25 each:
Percent Change
In percent-change questions, you will need to determine how a percent increase or decrease affects the values given in the question. Sometimes you will be given the percent change, and you will have to find either the original value or new value. Other times, you will be given one of the values and be asked to find the percent change. Take a look at this sample problem:
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A professional golfer usually has an average score of 72, but he recently went through a major slump. His new average is 20 percent worse (higher) than it used to be. What is his new average? | |
This is a percent-change question in which you need to find how the original value is affected by a percent increase. First, to answer this question, you should multiply 72 by .20 to see what the change in score was:
