Chapter 10  Objective 5.1  Exercises

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Solve.

1.  The height of a triangle is 3 m less than the length of the base. The area of the triangle is 20 m². Find the height of the triangle and the length of its base.

2.  The sum of the squares of two consecutive odd integers is thirty-four. Find the two integers.

3.  Five times an integer plus three times the square of the integer is twenty-two. Find the integer.

4.  The difference between the squares of two consecutive odd integers is thirty-two. Find the two integers.

5.  An old pump requires 6 h longer to empty a pool than does a new pump. With both pumps working, the pool can be emptied in 4 h. Find the time required for the new pump, working alone, to empty the pool.

6.  A small air conditioner requires 16 min longer to cool a room 4° than does a larger air conditioner. Working together, the two air conditioners can cool the room 4° in 6 min. How long would it take each air conditioner, working alone, to cool the room 4°?

7.  An old copier takes 15 min longer to copy a report than does a second, newer model. With both copiers working, the report can be printed in 18 min. How long would it take each copier, working alone, to copy the report?

8.  The rate of a corporate jet in calm air is 225 mph. Flying with a wind, the plane can fly 1000 mi in one hour less time than is required to make a return trip of 1000 mi. Find the rate of the wind.

9.  A car travels 240 mi. A second car, traveling 12 mph faster than the first, makes the same trip in 1 h less time. Find the speed of each car.

10.  A boat traveled 60 mi down a river and then returned. The total time for the round trip was 5 h, and the rate of the current was 5 mph. Find the rate of the boat in still water.

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