1. If one painter can paint a house in 4 days and another painter can paint a house in 7 days, how many days will it take them working together? 2. A car and a motorcycle both leave at the same point at the same time and travel in the same direction. The car travels at an average rate of 55 mph and the motorcycle travels at an average rate of 40 mph. How long will it take before the vehicles are 25 miles apart?

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Step-by-step explanation:

1. Add the rates in terms of houses per day.

  1/4 + 1/7 = (7+4)/28 = 11/28

Then the time required in terms of days per house is the reciprocal of this:

  28/11 = 2 6/11 . . . . days to paint a house, working together

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2. Each hour, the vehicles separate by 55 -40 = 15 miles. Then the time required for a separation of 25 miles is ...

  time = distance/speed = (25 mi)/(15 mi/h_ = 5/3 h = 1 2/3 h

The vehicles will be separated by 25 miles after 1 2/3 hours.

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step-by-step explanation: