jack can mop a ware house in ten hours. one day his friend Jimmy helped him and it only took 4.44 hours. How long would it take Jimmy to do it alone?

Answer 1

let Jimmy's rate be 1/x
Jack's rate = 1/10
combined rate = 1/x + 1/10 = (x+10)/(10x)

1/( (x+10)/(10x) ) = 4.44
10x/(x+10) = 4.44
10x = 4.44x + 44.4
5.56x = 44.4
x = 7.9856

Jimmy alone would take 7.99 hrs or appr 8 hrs

combined rate = 1/10 + 1/8 = 9/40
time at combined rate = 1/((9/40)) =40/9 = 4.4444....
ok then!