Sue can shovel snow from her driveway in 35 minutes. Bill can do the same job in 50 minutes. How long will it take Sue and Bill to shovel the driveway if they worked together.
(1/35) + (1/50) T
T=1 (1/35) + (1/50)=
Is the answer: 21.25
exactly right, you add the rates.
To find the time it will take Sue and Bill to shovel the driveway together, you need to calculate the sum of their individual rates.
Sue can shovel the driveway in 35 minutes, so her rate is 1/35 of the job per minute.
Bill can shovel the driveway in 50 minutes, so his rate is 1/50 of the job per minute.
To find the combined rate, you add their individual rates: 1/35 + 1/50.
To add these fractions, you need to find a common denominator. In this case, the common denominator is 1750 (50 * 35).
Now, you can rewrite the fractions with the common denominator: (50/1750) + (35/1750).
Adding the fractions gives you: 85/1750.
Therefore, when Sue and Bill work together, they can complete 85/1750 of the job in one minute.
To find the time it will take them to complete the entire job, you divide one by the combined rate: T = 1 / (85/1750).
To simplify, you can flip the fraction and multiply: T = 1750/85.
Dividing 1750 by 85 gives you approximately 20.59.
Therefore, it will take Sue and Bill approximately 20.59 minutes to shovel the driveway together.
Let's break down the problem. We are given that Sue can shovel the driveway in 35 minutes, and Bill can do it in 50 minutes. To find out how long it would take them to shovel the driveway together, we can add up their individual rates of work.
The rate at which Sue shovels the driveway is 1/35 of the driveway per minute. Similarly, the rate at which Bill shovels the driveway is 1/50 of the driveway per minute.
To find the combined rate at which they work together, we add up their individual rates:
(1/35) + (1/50)
To add fractions, we need a common denominator, which in this case is 35 * 50 (1750).
Now, let's convert the fractions to have the same denominator:
(50/1750) + (35/1750)
Combining the fractions:
(50 + 35) / 1750
Simplifying:
85 / 1750
To find out how long it would take them to shovel the driveway together, we can invert this fraction and multiply it by the total amount of work, which in this case is 1750 (since the fraction 85/1750 represents their combined rate per minute).
T = (1750 / 85)
Calculating this value gives us approximately 20.588, which means it would take Sue and Bill about 20.588 minutes to shovel the driveway together.
So the answer is not exactly 21.25, but rather 20.588 minutes.