Question

Fido can chew a strip a rawhide at a rate of five inches per minute. Fluffy can chew a strip of

rawhide at a rate of two inches per minute. Fluffy starts chewing on a long strip of rawhide, and six minutes
later, Fido starts chewing on the other end. Each of them chews until all of the rawhide is gone, and in the
end they have each consumed half of the original piece of rawhide. How long was the original strip of
rawhide?

Answer 1

Let the length of the original strip of rawhide be L inches.

Fluffy chews the rawhide for 6 minutes, so she chews a length of 6 x 2 = 12 inches.

Let the length of rawhide left be (L - 12) inches.

Fido chews the remaining rawhide, so he chews a length of 5x minutes, where x is the number of minutes he chews. The total length of rawhide he chews is (L - 12) - 5x.

Fido and Fluffy chewed half of the rawhide each, so they each chewed a length of L/2 inches.

Putting it all together:

Fluffy chews a length of 12 inches in 6 minutes, so her chewing rate is 2 inches per minute.

Fido chews a length of (L/2 - 12) inches in x minutes, so his chewing rate is (L/2 - 12)/x inches per minute.

In total, they chewed a length of L/2 inches.

We can write an equation to express the total length of rawhide they chewed:

12 + (L/2 - 12)/x * (x + 6) = L/2

Simplifying this equation:

12 + (L/2 - 12)(1 + 6/x) = L/2

Multiplying both sides by 2:

24 + (L - 24)(1 + 6/x) = L

Expanding the brackets:

24 + L - 24 + 6L/x - 6 = L

Simplifying:

6L/x = 6

L = x

So the original strip of rawhide was 6 x 2 = 12 inches long.