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?
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!