Hi Ellen. You have to assume the sisters can work together at full speed without interfering with each other. Hope the dog is easy-going!

Think about the question this way:

The first girl can do 1 full job alone in 45 minutes. That means her speed is 1 job in 45 minutes (1/45).

Her sister can do 1 full job alone in 60 minutes, so her speed is 1 job in 60 minutes (1/60).

If you add these speeds together, you get the combined speed:

1/45 + 1/60 = x

Now remember, the number of jobs divided by the speed gives you the total time. Since the girls are still doing just one job, you just divide 1 by x to answer the question.

Here's another example:

Pat takes 25 minutes to wash the car when he works alone. Paul takes 15 minutes to wash the car when he works alone. How long will it take if they cooperate and work together?

x
= 1/25 + 1/15
= 3/75 + 5/75
= 8/75

next, I divide the number of jobs by x to find the total time. There's still just one car to wash, so
1 / (8/75) = 75/8 = 9 5/8 = 9.625 minutes.

You can use decimals if you prefer that to fractions - you will get the same answer.

Cheers,
Stephen La Rocque

A girl can shampoo the dog, clean his ears, and clip his nails in 45 minutes.
Her sister can do it in 60 minutes.
How long will the job take it they work together?

I'd like to amplify a point that Stephen made. This problem is based on unrealistic assumptions! Not every task can be split among two or more people efficiently. Lewis Carroll (in his daytime personality as Charles Dodson, maths tutor at Christ Church College, Oxford), had a problem along the lines of

If it takes two men ten hours to build a wall, how long would it take twelve hundred men?

Students would calculate the answer as "one minute". Dodson would gently inform they that they were wrong; most of them could not even get near the wall to help!

A particularly silly example of my own invention:

If I can soft-boil an egg in three minutes, and a person in Denver, Colorado needs four minutes, how long does it take if we work together?

Good Hunting!
RD