Work-time problems?

Question

Ben and Bill are creating a new internet homepage. working alonr, Bill could do the job in 14 hours. it takes only 6 hours if they work together. how long would Ashley take to create the homepage alone?

Answer 1

Hi Lynn, lets start by assuming you have the names mixed up. Then the work equation becomes:

 

1 / 14 + 1 / x = 1 / 6

 

Where: 1 / 14 is the amount of work Bill can do in one hour, 1 / x is the amount of work Ashley can do in one hour, and finally, 1 / 6 is the amount of work the two of them can do in one hour.

 

Clear the fractions:

 

Multiply the entire equation by: 14 * 6 * x giving:

 

6x + 14 * 6 = 14x

 

Subtract 6x from both sides:

 

84 = 8x

 

Divide both sides by 8:

 

x = 10.5

 

It would take Ashley 10.5 hours to complete the job alone.

 

Questions?

Answer 2

I'm going to assume there's a typo in your question and that the end should be "how long would Ben take to create the homepage alone?"

 

We need to remember that, when determining how long it takes two people to accomplish a goal working together,

1/Ben + 1/Bill = 1/together

 

Let's fill in what we know.

1/14 + 1/Ben = 1/6

 

Let's make B = Ben

1/14 + 1/B = 1/6

 

Rearrange the terms to isolate the B

1/6 - 1/14 = 1/B

 

14-6          1

------  =    --

14•6         B

 

The reciprocal of this is

 

B = 14•6   = 84

      ------     ---

      14-6       8

 

It would take B(Ben) 10.5 hours working alone to create the homepage.