Amy can clean the house in 7 hours When she works with Tom the job takes 5 hours How long would it take Tom working by himself to clean the house?

Answer 1

Assuming that each of Amy and Tom works at a constant rate, in units of fractions of the house per hour, irrespective of the amount of cleaning remaining to be done and that the work is sufficiently nearly uniform that either Amy and Tom can complete each part of it at his or her own constant rate, then if Amy's rate is designated by a and Tom's rate by t, then 7a = 1 and 5a + 5t = 1. subtracting the second of these equations from the first yields 2a - 5t = 0, t = (2/5)a. Therefor, Tom works only 2/5 as fast as Amy, so that Tom by himself would require 7/(2/5) = 7(5/2) or 17-1/2 hours to clean the house by himself.