Question

Chloe can type a story in 6 hours. If Molly helps her, they finish typing the story in 4 hours. Find how long it would take Molly to type the story on her own.

Answer 1

Answer:

12 hours

Step-by-step explanation:

This is a rate question.

Since Chloe can type a story in 6 hours, her rate is 1 story per 6 hours or 1/6.

Together, with Molly, they can type a story in 4 hours. So their rate is 1 story per 4 hours or 1/4.

Since we don't know Molly's time to type the story, we'll call her time x.

We can set this up as an equation as follows:

1/6 + 1/x = 1/4

You need a common denominator, which is 12x to solve this.

1/6 needs to be multiplied by 2x/2x

1/x needs to be multiplied by 12/12

1/4 needs to be multiplied by 3x/3x

So the equation becomes: 2x/12x + 12/12x = 3x/12x

Since all terms have a denominator of 12x, they cancel out. (It's because if you want to get rid of the 12x on the right side, we multiply both sides by 12x, which would cancel out that common denominator in both terms on the left side).

Now the equation is 2x + 12 = 3x

Put the like terms together and solve!

I'd suggest moving the variable stuff to the right. So we'll subtract 2x from both sides.

Now the equation is 12 = x and you're done!

Molly's typing time is 12 hours.

You may think that since Molly's time is twice as long as Chloe's, she would slow her down, but that's not the case! As soon as Molly starts helping, their together time is reduced, no matter how slow Molly's typing time is. (Sorry Molly!)