Rational Expression Word Problem

Question

Jamar and Kerry are laying a hardwood floor. Working alone, Jamar can do the job in 20 hours. If the two of them work together, they can complete the job in 12 hours. How long would it take Kerry to lay the floor working alone?

 

In this problem, let x=the time it would take Kerry working alone

Answer 1

1.  Set up the rational expression.

 

1/20 + 1/x = 1/12

 

2.  Find the least common denominator of 12, 20 and x.  LCD = 60x

 

3.  Multiply the LCD on both sides.

 

60x[1/20 + 1/x] = 60x[1/12] ⇒ 60x/20 + 60x/x = 60x/12 ⇒ 3x + 60 = 5x

 

4.  Subtract 3x from both sides.  ⇒  60 = 2x

 

5.  Divide both sides by 2.  ⇒  x = 30 hours

 

It will take Kerry 30 hours by himself to lay a hardwood floor.