Frank can wash the car in 2/3 the time his younger brother , joe can wash the car. They worked together and washed the car in 40 minutes.

Question

How long would it have taken  each boy working separately? I have the answer as 100. can you show me how to work and get that answer. thank you

Answer 1

J -  Joe's time to wash

 

b -  Brother's time.

 

  J = (2/3) b 

 

     1  + 1  =  1 

     J      b     40

 

   1        + 1    = 1 

  (2b/3)      b      40     

 

  3/2b  + 1/b =  1/40

 

   3/2b + 2/2b = 1/40

 

     5/2b = 1/40

 

      2b = 200

 

        b = 100 / minutes

 

        J = 2(100)/ 3 = 67 minutes

 

 

 

 

  

Answer 2

To solve this type problem you always have to represent how fast the person works as a fraction. For example if a person can wash a car in 6 hours then you would represent that as 1/6.

 

For this problem:

 

The younger brothers speed is 1/x

Franks speed is 1/ (2/3)x

and the total time is 1/40

 

the equation would be 1/x + 1 / (2/3)x = 1/40

 

you can not add the fractions unless you have a common denominator which would be 40x, so multiply the entire equation by 40x ( you will notice the x will cancel out of the first two terms)

 

this gives 40 + 60 =x  therefore, x is equal to 100

 

Since x was how long the younger brother took alone, Frank can wash it in 2/3 of that speed or about 67 minutes