Question

It takes Brian 15 hours longer to build a model car than it takes John. If they work together, they can build the model car in 4 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Brian to build the car on his own.

Answer 1

    When they work together, it takes John 1/x hours and it takes Brian 1/(x+15) hours to complete 1/4 of the model.
   1/x + 1/( x+15 ) = 1/4  / · x ( x+15 )
    x+15 + x = x ( x+15 ) /4      / · 4
    8 x + 60 = x² + 15 x
    x² + 15 x - 8 x - 60 = 0
    x² + 7 x - 60 = 0
    x² + 12 x - 5 x - 60 = 0
    x · ( x + 12 ) - 5 ·( x+ 12 ) = 0
    ( x + 12 ) · ( x - 5 ) =0
    x = - 12  ( not accepted ) or  x = 5
    The time taken by Brian:  5 + 15 = 20 hours