Question

Three dogs can eat 3 bones in 3 days. If this efficiency is followed, how many bones can 9 dogs eat in 9 days?

Answer 1

We can start by using the formula:

Efficiency = Work / Time

where Efficiency is the rate at which the dogs can eat bones, Work is the number of bones that can be eaten, and Time is the number of days.

From the given information, we know that:

Efficiency = 3 bones / 3 dogs / 3 days
Efficiency = 1 bone / 1 dog / 1 day

This means that one dog can eat one bone in one day, or that the efficiency is 1 bone per dog-day.

To find out how many bones 9 dogs can eat in 9 days, we can use the same formula:

Efficiency = Work / Time

where Efficiency is still 1 bone per dog-day, Time is 9 days, and we want to find out Work, which is the number of bones.

Work = Efficiency x Time x Number of dogs

Work = 1 bone / dog-day x 9 days x 9 dogs

Work = 81 bones

Therefore, 9 dogs can eat 81 bones in 9 days if they maintain the same efficiency as 3 dogs eating 3 bones in 3 days.

Answer 2

If three dogs can eat three bones in three days, we can assume that each dog eats one bone in three days. Therefore, in one day, one dog can eat one-third of a bone.

If nine dogs were to eat in the same efficiency, we can multiply the number of dogs by the fraction of bones each can eat per day. So, nine dogs can eat 3 times more than 3 dogs in a day, which is 3 x 3 = 9 bones. In one day, each dog can eat one-third of the bone, and therefore nine dogs will eat 9 x 1/3 = 3 bones.

This means that in nine days, nine dogs can eat 9 x 3 = 27 bones.