Abigail and Bailey wash dogs to make extra money. Abigail can wash all of the dogs in 5 hours. Bailey can wash all the dogs in 3 hours. How long will it take them to wash the dogs if they work together?
Ab's rate --- 1/5
Bail's rate ---- 1/3
combined rate = 1/5 + 1/3 = 8/15
combined time = 1/(8/15) = 15/8 hrs
= 1 7/8 hrs
To find out how long it will take Abigail and Bailey to wash the dogs if they work together, we can use the formula:
1 / total time = 1 / Abigail's time + 1 / Bailey's time
Substituting the given values:
1 / total time = 1 / 5 hours + 1 / 3 hours
Now, we need to find the common denominator:
1 / total time = (3 / 15) + (5 / 15)
Adding the fractions:
1 / total time = 8 / 15
To solve for the total time, we need to take the reciprocal of both sides of the equation:
total time = 15 / 8
So, it will take them approximately 1 hour and 52.5 minutes to wash the dogs if they work together.
To find out how long it will take Abigail and Bailey to wash the dogs if they work together, you need to determine their combined work rate.
Let's start by calculating the work rate of each person. Abigail can wash all the dogs in 5 hours, so her work rate is 1/5 dogs per hour. Bailey can wash all the dogs in 3 hours, so his work rate is 1/3 dogs per hour.
To determine their combined work rate, you add their individual work rates: 1/5 + 1/3 = 3/15 + 5/15 = 8/15 dogs per hour.
Now, to find out how long it will take both of them to wash the dogs, you divide the total amount of work (which is washing all the dogs) by their combined work rate.
Since their combined work rate is 8/15 dogs per hour, you divide the total work (1 dog) by 8/15:
1 / (8/15) = 1 * (15/8) = 15/8 hours.
Therefore, it will take them 15/8 hours, or 1.875 hours (1 hour and 52.5 minutes) to wash the dogs if they work together.