Sue can shovel snow from her driveway in 45 minutes. Bill can do the same job in 65 minutes. How long would it take Sue and Bill to shovel the driveway if they worked together?
Add up the "driveways per minute" of the two. That times the time T must equal 1 driveway
1 = (1/45 + 1/65) T
T = 1/(1/45 + 1/65)= 26.6 minutes
To determine how long it would take Sue and Bill to shovel the driveway together, we can use the concept of work rates.
Let's denote Sue's work rate as S and Bill's work rate as B.
Sue can shovel the driveway in 45 minutes, so her work rate would be 1/45 of the driveway per minute (since she completes 1 driveway in 45 minutes).
Bill can shovel the driveway in 65 minutes, so his work rate would be 1/65 of the driveway per minute (since he completes 1 driveway in 65 minutes).
To find the combined work rate when they work together, we can add their individual work rates:
S + B = 1/45 + 1/65
To add these fractions, we need to find a common denominator, which is 45 * 65 = 2925.
Multiplying each fraction by the appropriate factor to get a common denominator, we have:
S + B = (65/2925) + (45/2925)
S + B = 110/2925 + 45/2925
S + B = 155/2925
S + B = 31/585
Therefore, when Sue and Bill work together, their combined work rate is 31/585 of the driveway per minute.
To find the time it would take them to shovel the driveway together, we can use the formula:
Time = 1 / Combined Work Rate
Time = 1 / (31/585)
Time = 585 / 31
Time ≈ 18.87 minutes
So, it would take Sue and Bill approximately 18.87 minutes to shovel the driveway together if they both work at their individual rates.
To find out how long it would take Sue and Bill to shovel the driveway together, we can use the concept of work rates. The work rate represents the amount of work done in a given unit of time.
First, let's calculate the work rate for Sue and Bill individually. Sue can shovel the entire driveway in 45 minutes, so her work rate is equal to 1 driveway / 45 minutes, or 1/45 driveways per minute.
Similarly, Bill can shovel the entire driveway in 65 minutes, so his work rate is equal to 1 driveway / 65 minutes, or 1/65 driveways per minute.
To determine how long it would take for them to complete the job together, we can add their work rates.
Sue's work rate + Bill's work rate = Their combined work rate
1/45 + 1/65 = 65/2925 + 45/2925 = (65 + 45) / 2925 = 110 / 2925 = 2/55 driveways per minute
Now, to find the time it would take for Sue and Bill to complete the job together, we can divide the work needed (1 driveway) by the combined work rate.
Time = Work / Combined work rate
Time = 1 / (2/55) = 1 * (55/2) = 55/2 = 27.5 minutes
Therefore, it would take Sue and Bill 27.5 minutes to shovel the driveway if they worked together.
Sue = 1/45
Bill = 1/65
Together = 1/x
1/45 + 1/65 = 1/x
We have a fractional equation.
Solve for x.
What is the LCD of 45, 65 and x?
It 585x.
We now multiply every term on BOTH sides of the fractional equation by the LCD.
(1/45)(585x) + (1/65)(585x) = (1/x)(585x)
13x + 9x = 585
22x = 585
Divide BOTH sides of the linear equation (not fractional anymore) by 22 to find x.
x = 585/22
x = 26.59
How long would it take Sue and Bill to shovel the driveway if they worked together?
Answer: 26 hours and 59 seconds, which we can also accept as 27 hours.
Done!