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math word problem

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?
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2 Answers

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. 
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

Comments

Would the person who gave me the thumbs down like to explain what exactly is wrong with this solution ?
This is how you solve these types of problems using algebra. Suppose the problem was as stated:
Susan waxes her car in 2 6/7 hrs. When she works together with Helga, they can wax the car in 1 1/3 hrs.
How long would it take Helga to wax the car alone ? Solving this one would be difficult without algebra !