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A positive integer is twice another. The sum of the reciprocals of the two positive integers is . Find the two integers

Application problems including rational equations.

Set up a rational equation and then solve the following problems.

1. A positive integer is twice another. The sum of the reciprocals of the two positive integers is . Find the two integers.

2. A positive integer is twice another. The difference of the reciprocals of the two positive integers is Find the two integers.

3. John can jog twice as fast as he can walk. He was able to jog the first 5 miles to his grandmother’s house, but then he tired and walked the remaining 2 miles. If the total trip took 0.9 hours, then what was his average jogging speed?

4. A bus averages 2 miles per hour faster than a motorcycle. If the bus travels 165 miles in the same time it takes the motorcycle to travel 155 miles, then what is the speed of each?

5. Jane can paint the office by herself in 7 hours. Working with an associate, she can paint the office in 3 hours. How long would it take her associate to do it working alone?

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