it takes 4 hr for 8 cook to prepare a dinner. how long would it take for 7 cooks? inverse or direct variation?
To determine whether the relationship between the number of cooks and the time taken is an inverse or direct variation, we need to consider the given information. Inverse variation occurs when an increase in one variable (the number of cooks) causes a decrease in another variable (the time taken). Direct variation occurs when an increase in one variable causes an increase in the other variable.
In this case, we are given that it takes 4 hours for 8 cooks to prepare dinner. To find out how long it would take for 7 cooks, we can set up a proportion:
8 cooks / 4 hours = 7 cooks / x hours
To solve for x (the time taken for 7 cooks), we can cross-multiply:
8 * x = 4 * 7
8x = 28
Dividing both sides by 8, we find:
x = 3.5
Therefore, it would take 7 cooks approximately 3.5 hours to prepare the dinner.
Since an increase in the number of cooks causes a decrease in the time taken, this relationship is an inverse variation.