Kevin stuffs shrimp in his job as a seafood chef. He can stuff 1200 shrimp in 4 hours. When his sister helps him, they can stuff 1200 shrimp in 3 hours. If kevin gets sick, how long will it take his sister to stuff 600 shrimp?

consider 1200 shrimp One job.

1/3 = 1/4 + 1/t
t = 12
so, sis can stuff 1200 shrimp in 12 hours.
600 shrimp in 6 hours

To solve this, we can use the concept of "man-hours." A man-hour is the amount of work performed by one person in one hour. Let's calculate the number of man-hours required to stuff the shrimp in each case:

When Kevin works alone:
Man-hours = shrimp stuffed / shrimp stuffed per hour
Man-hours = 1200 / (1200/4) = 4 man-hours

When Kevin and his sister work together:
Man-hours = shrimp stuffed / shrimp stuffed per hour
Man-hours = 1200 / (1200/3) = 3 man-hours

Now, we can determine how long it would take Kevin's sister to stuff 600 shrimp by herself:

Shrimp stuffed per hour when Kevin and his sister work together = 1200 / 3 = 400 shrimp/hour

Time required for sister to stuff 600 shrimp = shrimp stuffed / shrimp stuffed per hour
Time required for sister to stuff 600 shrimp = 600 / 400 = 1.5 hours

Therefore, it would take Kevin's sister 1.5 hours to stuff 600 shrimp by herself.

Let's start by finding the rate at which Kevin can stuff shrimp alone. We can do this by dividing the number of shrimp (1200) by the number of hours (4).

Rate of Kevin's shrimp stuffing = 1200 shrimp / 4 hours = 300 shrimp/hour

Next, let's find the combined rate at which Kevin and his sister can stuff shrimp. We can do this by dividing the number of shrimp (1200) by the number of hours (3).

Combined rate of Kevin and sister's shrimp stuffing = 1200 shrimp / 3 hours = 400 shrimp/hour

Since we know Kevin's sister can stuff shrimp at a rate of 400 shrimp/hour, we can find out how long it will take her to stuff 600 shrimp by dividing the number of shrimp (600) by the rate (400 shrimp/hour).

Time required for Kevin's sister to stuff 600 shrimp = 600 shrimp / 400 shrimp/hour = 1.5 hours

Therefore, it will take Kevin's sister 1.5 hours to stuff 600 shrimp on her own.