# Kevin stuffs shrimp in his job as a seafood chef. He can stuff 1,550 shrimp in 6 hours. When his sister helps him, they can stuff 1,550 shrimp in 4 hours. If Kevin gets sick, how long will...

Kevin stuffs shrimp in his job as a seafood chef. He can stuff 1,550 shrimp in 6 hours. When his sister helps him, they can stuff 1,550 shrimp in 4 hours. If Kevin gets sick, how long will it take his sister to stuff 775 shrimp?

One could also solve this problem by setting up an equation:

Total (Kevin's and his sister's rate) = Kevin's rate + sister's rate.

Their total rate is 1550/4 shrimp per hour.

Kevin's rate is 1550/6 shrimp per hour.

The sister's rate is not given, but if it take her x hours to stuff 775 shrimp, her rate can be expressed as 775/x shrimp per hour.

So the equation for total rate becomes:

`1550/4 = 1550/6 + 775/x`

To solve, multiply both sides by the common denominator, 12x:

`12x*1550/4 = 12x*1550/6 + 12x*775/x`

Canceling all common factors gives us

`3x*1550 = 2x*1550 + 12*775`

Now bring all x's to the left side:

`3x*1550 - 2x*1550 = 12*775`

`x*1550 = 12*775`

Divide both sides by 1550:

`x = (12*775)/1550 = 12/2 = 6`

**It will take Kevin's sister 6 hours to stuff 775 shrimp.**

Kevin stuffs 1550 shrimp in 6 hours. This means that Kevin stuffs `` shrimps per hour. (Take the total number of shrimp divided by the total number of hours.)

Kevin and his sister stuff 1550 shrimp in 4 hours; this means that they stuff 387.5 shrimps per hour together.

Kevin's sister accounts for the additional shrimps per hour. Thus her hourly rate is found by `` shrimps per hour.

We can divide 775 by `` to get 6. (Alternatively, recognize that `` or the sister does 775 shrimps every 6 hours.)

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It will take Kevin's sister 6 hours to do 775 shrimps

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We assume that Kevin and his sister are working independently. That is, they are not working on a sort of assembly line.