SOLUTION: Kevin stuffs shrimp in his job as a seafood chef. He can stuff 1,500 shrimp in 4 hours. When his sister helps him, they can stuff 1,500 shrimp in 3 hours. If Kevin gets sick, how l

Question 1174114: Kevin stuffs shrimp in his job as a seafood chef. He can stuff 1,500 shrimp in 4 hours. When his sister helps him, they can stuff 1,500 shrimp in 3 hours. If Kevin gets sick, how long will it take his sister to stuff 750 shrimp?
Found 4 solutions by Theo, MathTherapy, ikleyn, josgarithmetic:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
rt=q
r = rate
t = time
q = quantity

kevin stuffs 1500 shrimp in 4 hours.
his equation becomes r * 4 = 1500
solve for r to get:
r = 1500/4 = 375
that means he stuffs shrimp at a rate of 375 per hour.

when his sister helps him, they can stuff 1500 shrimp in 3 hours.
when they work together, their rates are additive.
let r = her rate.
their combined rate is r + 375
r is her rate, 375 is his rate.
formula becomes:
(r + 375) * 3 = 1500
solve for r + 375 to get:
r + 375 = 500
solve for r to get:
r = 500 - 375 = 125
her rate is 125 stuffed shrimp per hour.

confirm by replacing r with her rate to get:
(125 + 375) * 3 = 1500
combine like terms and simplify to get:
500 * 3 = 1500 becomes 1500 = 1500
this confirms the values are correct.

at 125 shrimps per hour, it would take his sister 750 / 125 = 6 hours to stuff 750 shrimp by herself.

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

Kevin stuffs shrimp in his job as a seafood chef. He can stuff 1,500 shrimp in 4 hours. When his sister helps him, they can stuff 1,500 shrimp in 3 hours. If Kevin gets sick, how long will it take his sister to stuff 750 shrimp?

Stuffing 1,500 is regarded as 1 JOB Stuffing 750 is considered to be ½ of the JOB Let time it takes the sister to do the job by herself be S Then she can do of job in 1 hour Kevin can do the job by himself in 4 hours So, he can do ¼ of job in 1 hour Working together, they both can do the job in 3 hours, so we the get: 12 + 3S = 4S ------ Multiplying by LCD, 12S Time it takes the sister to do the job by herself, or S = 12 hours If she can do entire job (stuffing 1,500 shrimp) in 12 hours, then she can complete

Answer by ikleyn(52817)   (Show Source): You can put this solution on YOUR website!
.

It is good arithmetic problem to be solved by 3rd - 4th grade student ARITHMETICALLY without using any equations.

Kevin stuffs 1500/4 = 375 shrimps per hour, working alone. With her sister, they stuff 1500/3 = 500 shrimps per hour. Hence, the sister stuffs 500-375 = 125 shrimps per hour, working alone. It means that the sister needs 750/125 = 6 hour to make this job alone.

Solved.

Answer by josgarithmetic(39621)   (Show Source): You can put this solution on YOUR website!
Kevin,
Kevin and sister,
Sister alone,

How long for his sister to stuff 750 shrimp?
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