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Question 767307: Two airplanes working together can take the necessary photographs to map to a certain region in 5 hours. After they had worked for 3 hours the first plane developed engine trouble and the second had to finish the job, requiring 4.5 hours of additional work. How long would it take each plane alone to do the job?
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! Working together, they can complete the job in 5 hrs
That means their combined rate is 1 job per 5 hrs -> r1 + r2 = 1/5 job/hr
After 3 hrs of working together, they have completed 3 hr * (1/5 job/hr) = 3/5 of the job
The remaining 2/5 of the job is completed by the 2nd plane in 4.5 hrs
Therefore, the rate of the 2nd plane is r2 = (2/5 job)/(4.5 hr) = (2/5)/(9/2) = 4/45 job/hr
r1 = 1/5 - r2 = 1/5 - 4/45 = 9/45 - 4/45 = 5/45 job/hr
So it would take the 1st plane 45/5 = 9 hrs and it would take the 2nd plane 45/4 = 11.25 hrs to complete the job alone
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