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Question 540598: Show an equation and a solution for the problem. It takes John 20 hours to paint a building. It takes Sam 15 hours to paint the same building. How long will it take for them to paint the building if they work together, with Sam starting one hour later than John? Round to the nearest tenth.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Show an equation and a solution for the problem. It takes John 20 hours to paint a building. It takes Sam 15 hours to paint the same building. How long will it take for them to paint the building if they work together, with Sam starting one hour later than John? Round to the nearest tenth.
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John's rate = 1/20 job/hr
Sam's rate = 1/15 job/hr
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Together rate = 1/x job/hr
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Equation:
rate + rate = together rate
1/20 + 1/15 = 1/x
3x + 4x = 60
x = 60/7 Time to do the jog together
Together rate = 7/60 job/hr
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Equation:
How long will it take for them to paint the building if they work together, with Sam starting one hour later than John? Round to the nearest tenth.
John work + together work = job done
(1/20) + (7/60)x hrs = 1 job
3 + 7x = 60
7x = 57
x = 57/7 = 8.1429 hrs. (time they work together)
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Cheers,
Stan H.
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