A positive integer is twice another.

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.

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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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