math word problem

Question

Susan can wax her car in 2 hr(s). When she works together with Helga, they can wax the car in thirty min(s). How long would it take Helga, working by herself, t0 wax the car?

Answer 1

Helga can wax the car by herself in 40 minutes.

 

Working together, Susan will wax 1/4 of the car in 30 minutes.  Helga will wax the other 3/4 of the car in 30 minutes. 

Answer 2

x= Helga's rate

(1/2)(1/2)+(1/x)(1/2)=1

1/4+(1/2x)=1

(4x)(1/4)+(4x)(1/2x)=4x(1)

x+2=4x

2=3x

x=2/3 hr

check:

assume we don't know how long it takes them to work together(x hrs)

(1/2)(x)+(1/(2/3))x=1

(1/2)x+(3/2)x=1

(4/2)x=1

2x=1

x=1/2 hr working together which is what was stated