It takes Dustin 2 hours to shovel the snow from his driveway and sidewalk. It takes his sister 3 hours to shovel the same area. How long will it take them to shovel the walk if they work together?
Dustin = 1 driveways / 2 hours
sister = 1 driveway / 3 hours
Dustin + sister = ( 1/2 + 1/3)driveway / hours
= 3/6 + 2/6 = 5/6 driveways/hour
invert for 6/5 = 1 1/5 hours/ driveway
To determine how long it will take them to shovel the walk if they work together, we can use the formula:
Time = (Work / Rate)
Let's say the work is measured in terms of the entire area to be shoveled.
To find the rates, we can calculate the area each person shovels per hour:
Dustin's rate: 1 area / 2 hours = 1/2
Sister's rate: 1 area / 3 hours = 1/3
Combined rate: Dustin + Sister = 1/2 + 1/3
To simplify the equation, we find a common denominator:
1/2 + 1/3 = 3/6 + 2/6 = 5/6
Now, we have the combined rate, which is 5/6.
To find the time it takes to complete the work together, we use the formula again:
Time = (Work / Rate)
Time = 1 area / (5/6 rate)
Time = 1 area * (6/5 rate)
Time = 6/5 hours
Therefore, it will take them 6/5 hours, which is equivalent to 1.2 hours or 1 hour and 12 minutes, to shovel the walk if they work together.
To find out how long it will take for Dustin and his sister to shovel the walk together, we need to calculate their combined rate.
Dustin takes 2 hours to shovel the walk, which means he can shovel 1/2 of the walk in one hour (since he can complete the whole walk in 2 hours). Similarly, his sister takes 3 hours to shovel the walk, meaning she can shovel 1/3 of the walk in one hour.
To find their combined rate, we add their individual rates together: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
This means that together, they can complete 5/6 of the walk in one hour. To find out how long it will take for them to complete the entire walk, we divide the total work (1) by their combined rate (5/6):
1 / (5/6) = 1 * (6/5) = 6/5.
Therefore, it will take them 6/5 hours or 1 hour and 12 minutes to shovel the walk together.