It takes a man 5 hours to wash and wax the family car. If his teenage son helps him, it only takes 3 hour(s). ....?

It takes a man 5 hours to wash and wax the family car.

If his teenage son helps him, it only takes 3 hours.

How long would it take the son,

working alone, to wash and wax the car?

1/3 - 1/5 = 1/x

2/15 = 1/x

x = 15/2

It would take 7 hours 30 minutes for the son

to wash and wax the car working alone.

Let 'm' be man and 's' be son

m = 1/5 task in 1 hour

m + s = 1/3 task in 1 hour

difference (m+s - m) is 5/15 - 3/15

therefore s = 2/15ths task in 1 hour

15/2 x 1 = 7.5

It would take the son 7 and half hours

w = c / t

c = 1 car washed & waxed

tf = father's work time = 5.00 hours

wf = father's work rate = 1/tf = 0.20 c/h = car per hour

t = combined father & son work time = tf + ts = 3.00 hours

w = combined work rate = 1/(tf + ts) = 0.33 c/h = car per hour

ws = son's work rate = to be determined

ts = son's work time = to be determined

w = wf + ws

w - wf = ws

ws = w - wf

ws = 0.33 c/h - 0.20 c/h

ws = 0.13 c/h = car per hour

ts = son's work time = 1/ws = 7.5 hours