If it takes 4 minutes to fill a bucket with one tap and 6 minutes to fill the bucket with another tap. Using both taps how many seconds will it take to fill the bucket?
rate of 1st tap = 1/4
rate of 2nd tap = 1/6
rate of both taps = 1/4 + 1/6 = 5/12
time at combined rate = 1/(5/12) = 12/5 or 2.4 minutes
Basically see how many gal per minute or what ever unit of time you wish. Once you get what each tap fills per minute you add them.
Tap 1: per minute tap one has 1/4 a gal
Tap 2: per minute tap two has 1/6 a gal
Add them together 3/12+2/12= 5/12
So in one minute 5/12 of a gallon will be filled.
To see how many minutes it will take for a full gallon you have 1 gal divide amount per minute and you have 12/5, 2+2/5 or 2.4 minutes.
To answer do 69 x the highest amount divided by 420
To determine the time it takes to fill the bucket using both taps, you can take the reciprocal of the filling rate for each tap and add them together. Let's break down the process step by step:
1. Calculate the filling rate for each tap:
- The first tap takes 4 minutes to fill the bucket, so its filling rate is 1 bucket/4 minutes, or 1/4 buckets per minute.
- The second tap takes 6 minutes to fill the bucket, so its filling rate is 1 bucket/6 minutes, or 1/6 buckets per minute.
2. Find the combined filling rate of both taps:
- Add the filling rates of both taps together: 1/4 + 1/6 = 3/12 + 2/12 = 5/12 buckets per minute.
3. Convert the filling rate to seconds:
- Since there are 60 seconds in a minute, multiply the filling rate by 60 to convert it to buckets per second: (5/12) * 60 = 5 * 5 = 25/12 buckets per second.
4. Calculate the time to fill the bucket:
- Take the reciprocal of the combined filling rate to find the time it takes to fill one bucket: 1 / (25/12) = 12/25 seconds per bucket.
Therefore, using both taps, it will take 12/25 seconds to fill the bucket.