Math Homework Help?

Question

When Lauren and Johnny worked together to rake the leaves in their backyard, it took them 6 hours. The last time the leaves needed raking, Johnny worked alone, and it took him 10 hours. If Lauren raked the leaves by herself, how long would it take her? (Only an algebraic solution will be accepted.)

Answer 1

Johnny rakes 1/10 of the yard in an hour.

Together they rake 1/6 of the yard in an hour.

So if we takes Lauren's rate as 1/L of the yard in an hour you have:

1 ... 1 .... 1
-- + --- = ---
L ...10 ... 6

1/L = 1/6 - 1/10
1/L = 5/30 - 3/30
1/L = 2/30
1/L = 1/15

L = 15

So Lauren would take 15 hours on her own.

Answer 2

Lauren rate = 1 yard in x hours

Jonny rate = 1 yard in 10 hours

Adding them

1/x + 1/10 = 1/6 {working together}

Multiply by LCD (60x)

60 + 6x = 10x
60 = 4x
15 = x {Lauren = 1 yard in 15 hours}

Check

1/15 + 1/10 = 2/30 + 3/30 = 5/30 = 1/6

Answer 3

In 1 hour, Johnny rakes 1/10 of the yard (since it takes him 10 hours to do one yard)
In 1 hour, Lauren rakes 1/x of the yard (since it takes her x hours to do one yard)

If they can do it together in 6 hours, the algebraic expression is:

6(1/10 + 1/x) = 1

Solve for x, and you'll have the number of hours it takes Lauren to rake the yard herself.

Answer 4

(10 + x) / 2 = 6

10 + x = 12
-10 -10

x = 2