Working together, 2 groomers can brush 8 horses in 3 hours. How many hours would it take 3 groomers to brush 12 horses at this rate?
2 groomers can brush 8 horses in 3 hours.
3 groomers can brush 12 horses in:
3*(3/2)*(12/8) hours.
3 hours
To find out how many hours it would take 3 groomers to brush 12 horses at the same rate, we need to use the concept of work.
Here's how you can solve this problem step-by-step:
1. Start by determining the amount of work required to brush the horses. In this case, it's 12 horses.
2. Next, determine the rate at which the groomers work. Since 2 groomers can brush 8 horses in 3 hours, we can determine their rate as follows:
- Rate of 2 groomers = Work / Time = 8 horses / 3 hours = 8/3 horses per hour.
3. Now, let's calculate how long it would take 3 groomers to brush 12 horses.
- We can set up a proportion using the following equation:
(Rate of 2 groomers) x (Time needed for 2 groomers) = (Rate of 3 groomers) x (Time needed for 3 groomers).
- Plugging in the given values, we have:
(8/3) x (3 hours) = (Rate of 3 groomers) x (Time needed for 3 groomers).
- Simplifying this equation, we find:
8 = (Rate of 3 groomers) x (Time needed for 3 groomers).
4. Since the rate of the 3 groomers would remain the same, we can rearrange the equation to solve for the time needed for 3 groomers:
- Time needed for 3 groomers = 8 / (Rate of 3 groomers).
5. Given that the rate of the 3 groomers is the same as the rate of the 2 groomers, which is 8/3 horses per hour, we can substitute it into the equation:
- Time needed for 3 groomers = 8 / (8/3) = 8 * (3/8) = 3 hours.
Therefore, it would take 3 groomers 3 hours to brush 12 horses at the same rate.