Question

Is this an inverse variation, or an direct variation: It takes 5 hours for 2 cooks to prepare food for a wedding rehearsal. How long will it take 8 cooks to prepare the dinner?

Answer 1

Inverse variation ; `8` cooks will take `1` hour and `15` minutes to prepare the diiner.

Explanation:

More cooks employed less hour will be taken to prepare the same

dinner. So it is inverese variation.Let the number of cooks be

`n` and `h` be the hours reqired. `:. n prop 1/h or n= k*1/h`

`:. k=n*h ; k` is the variation constant. `n=2 ,h=5`

`:. k=2*5 or k =10 ; n=8 :. 8*h=10 or h =10/8 = 1 1/4`

hour. Hence `8` cooks will take `1` hour and `15` minutes to

prepare the diiner [Ans]

Answer 2

It will now take `1 1/4` hours to cook the meal

Explanation:

In a direct variation (same as direct proportion) then, as one quantity INCREASES, the other also INCREASES.

In an inverse variation, as one quantity INCREASES, the other DECREASES.

Questions where a task of some kind has to be done are usually inverse variations, because the MORE people there are to do a task,the LESS time it will take.

This is just such a case.

In inverse variation, find the constant by multiplying the two quantities:

`x xxy = k`

`5 xx 2 = 10" "larr` hours `xx` cooks

`x xx 8 = 10" "larr` hours `xx` cooks

`x = 10/8 = 1.25`

It will now take `1 1/4` hours to cook the meal