10 chefs can prepare a meal for 536 people in 8 hours.Assuming that the chefs cook at the same rate

[samandar123]

10 chefs can prepare a meal for 536 people in 8 hours. Assuming that the chefs cook at the same rate and that the rate at which they cook remains constant throughout the preparation. Find the number of people 22 chefs can prepare a meal for in 5 hours.

 

[conway]

What is it that they are cooking? The rate can be constant, and the chefs can cook at the same rate. But food does not all cook at the same rate. 10 chefs can cook a brisket, all at the same rate. But a brisket takes longer to cook than macaroni and cheese.

 

[samandar123]

The questioner didn't mention it, cuz he might not have considered it important.

 

[Alonzo]

I figure 1 chef is good for 53.6 people in 8 hours = 6.7 people in 1 hour.

Then I get 22 * 6.7 = 147.4 people by 22 chefs in 1 hour = 5 * 147.4 = 737 people in 5 hours.

 

[conway]

The questioner didn't mention it, cuz he might not have considered it important.

Consider poor Alonzo's reply. The expression would yield different products depending on what it was they were cooking wouldn't it. That small bit of information is actually all important! If you wish it to be in line with reality.

Of course you have the option of keeping it purely absract. Then you are right. The question I pose is meaningless. You just "assume" a rate of cooking and you are done with it. Yet what is the point in asking such a question....if it is not going to be applied to reality.

 

[samandar123]

its answer is 737 in the book.
https://1drv.ms/i/c/7fcb4f584654896b/EZ01yvQeF6xDiJ7TO62sfXsBq72kMJ9EGzzgJ7Er4qdIwQ?e=jBaOKB
if the above link do not work then click below
https://u.pcloud.link/publink/show?code=XZRjq55ZpuVc8YSQK4XwuA6kJc0XyzfaLnaX

 

[samandar123]

I don't know what number to divide by or multiply by what number.because there are more than two variables involved.

 

[Alonzo]

I think I explained my calculation above clearly. What do you not get?

 

[samandar123]

I'm confused about the point in 53.6

 

[Alonzo]

536 / 10 = 53.6.

Of course, at the end we need to have an integer answer, not rounding, but rather the floor function, which truncates the fractional part. (Rounding, if up, would give a slightly bigger value than the chefs can handle.)

Question is - floor at each calculation, or wait until the end?

I'm not really sure, so I decided to wait until the end, which as it turned out was an integer answer anyway.

 

[samandar123]

@Alonzo.
now I understand it. i was thinking in different directions to solve it but not in the correct direction as you did it on your first attempt.
thanks.

 

[Alonzo]

These kinds of problems can be confusing. Thanks for posting it - a good refresher to solve it.

You say "your first attempt." Not so - my first reported attempt. I may have had false starts first.