Question

It takes Mom, Dad and Isabel two hours to shovel their driveway after a snow storm. If Dad worked alone, it would take him 4 hours to shovel the entire driveway by himself. If Isabel worked alone, it would take her twice as long as Dad. How long would it take Mom to shovel the driveway herself

Answer 1

8 hours

Explanation:

If two people shovel at the same rate, they can do the job in half the time.

We have ...

(Dad) + (Mom + Isabel) ⇒ 2 hours . . . . half as long as Dad alone

Dad ⇒ 4 hours

This tells us that ...

(Mom +Isabel) = 4 hours

We know that ...

Isabel ⇒ 2×4 hours = 8 hours . . . . twice as long as Mom + Isabel

So, we conclude ...

Mom ⇒ 8 hours

It would take Mom 8 hours to shovel the driveway herself.

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Additional comment

The rates add when expressed as driveways per hour.

total = Dad + Mom + Isabel

1/2 = 1/4 + 1/m + 1/(2·4)

1/m = 4/8 -3/8 = 1/8

m = 8 . . . . . it takes Mom 8 hours by herself.