Work = Rate * Time.
Assume Work = 1
1 = R * T
=> R = 1 / T
Jon can wax his car in 3 hours. Jim can do the same job in 5 hours. How long will it take if they work together?
John Time = t1 = 3
Jim Time = t2 = 5
Together time = T
Formula: (1 / t1) + (1 / t2) = 1 / T
1/3 + 1/5 = 1/T
T = 15/8
Derivation:
Work of John + Work of Jim = Total Work
Work = rate * Time
Rate of jon = 1/3
Rate of jim = 1/5
Applying the formula
T/3 + T/5 = T*R where R is combined Rate.
