Chris and Bob have a painting business. Chris has less experience and it takes him 4 hours longer than Bob to paint a fence. Working together they can paint a fence in 6 hours. How long does it take Chris to paint the fence by himself? Round your answer to the nearest tenth of an hour if necessary

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Jaycee Figueroa · Accepted Answer

Let the time taken by Bob to paint a fence be x hours. So, that of Chris becomes (x+4) hours.So, in x hours, bob can do 1 complete work (painting fence).In 1 hour, he can do       1    x   of complete work.Similarly, in 1 hour, Chris can do       1          x      +      4       of complete work.When both of them work together for 1 hour, they can finish       (          1      x        +          1              x        +        4              )   of complete work.Given that, in 6 hours they can do 1 complete work together. In 1 hour, they can do       1    6   of complete work.So,      1    x    +      1          x      +      4        =      1    6    ⇒            (      x      +      4      )      +      x              x      (      x      +      4      )        =      1    6    ⇒  6  (  2  x  +  4  )  =  x  (  x  +  4  )    ⇒  12  x  +  24  =      x    2    +  4  x  ⇒      x    2    −  8  x  −  24  =  0    ⇒  x  =  4  +  2      10    ,  4  −  2      10    ⇒  x  =  4  +  2      10    =  10.3    ⇒  x  +  4  =  14.3Thus, Bob takes 10.3 hours to paint a fence on his own while Chris takes 14.3 hours to do the same.

Chris and Bob have a painting business. Chris has less experience and it takes him 4 hours longer than Bob to paint a fence. Working together they can paint a fence in 6 hours. How long does it take Chris to paint the fence by himself? Round your answer to the nearest tenth of an hour if necessary

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