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 information 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:
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: Once you know the score change, then you should add it to his original average, since his new average is higher than it used to be: It is also possible to solve this problem by multiplying the golfer’s original score by 1.2. Since you know that the golfer’s score went up by twenty percent over his original score, you know that his new score is 120% higher than his old score. If you see this immediately, you can skip a step and multiply 72 1.2 = 86.4. Here’s another example of a percent-change problem:
A shirt whose original price was 20 dollars has now been put on sale for 14 dollars. By what percentage did its price drop?
In this case, you have the original price and the sale price and need to determine the percent decrease. All you need to do is divide the amount by which the quantity changed by the original quantity. In this case, the shirt’s price was reduced by 20 – 14 = 6 dollars. So, 620 = .3, a 30% drop in the price of the shirt. Double Percent Change A slightly trickier version of the percent-change question asks you to determine the cumulative effect of two percent changes in the same problem. For example:英语作文
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