



 
If James needs x hours to paint the house he paints 1/x houses per hour. Colleen paints 1/(x2) houses per hour. In 10 hours together they paint 10/x + 10/(x2) houses, but you're told this sum = 1 house, i.e., 10/x + 10/(x2) = 1. Cross multiply by x(x2) to get 10(x2) + 10x = x(x2), or
thus, using the general quadratic, x = (1/2)(22 ± sqrt(48480)) = (1/2)(22 ± sqrt(404)) which does not equal 21 in any way but it is close to it as sqrt404 is about 20 giving x about (1/2)(22+20) = 21. The answer is not 21 hours, but it's close. Penny  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 