Sue can shovel snow from her driveway in 40 minutes. Tom can do the same job in 35 minutes. How long would it take Sue and Tom to shovel the driveway if they worked together?
To find out how long it would take Sue and Tom to shovel the driveway if they worked together, we can calculate their combined rate of work.
Let's find their individual rates of work first:
Sue's rate of work: 1 driveway/40 minutes = 1/40 driveways per minute
Tom's rate of work: 1 driveway/35 minutes = 1/35 driveways per minute
Their combined rate of work is the sum of their individual rates:
Combined rate = Sue's rate + Tom's rate
Combined rate = 1/40 + 1/35
Now, let's find a common denominator for 40 and 35, which is 280.
Combined rate = (280/40) + (280/35)
= 7/1 + 8/1
= 15/1
Therefore, their combined rate is 15/1 driveways per minute.
This means that when Sue and Tom work together, they can shovel 15 driveways in 1 minute.
To find out how long it would take them to shovel 1 driveway, we just need to find the reciprocal of their combined rate:
Time = 1/combined rate
Time = 1/(15/1)
= 1 * (1/15)
= 1/15
Therefore, it would take Sue and Tom 1/15 of a minute or 1/15 minutes to shovel the driveway if they worked together.
In decimal form, this is approximately 0.067 minutes or 4 seconds (since there are 60 seconds in 1 minute).
So, it would take Sue and Tom approximately 0.067 minutes or 4 seconds to shovel the driveway if they worked together.
To find out how long it would take Sue and Tom to shovel the driveway together, we can use the concept of their individual work rates.
First, let's find the work rate of Sue. We know that she can shovel the whole driveway in 40 minutes. Therefore, Sue's work rate is 1 driveway / 40 minutes = 1/40 driveway per minute.
Similarly, Tom's work rate is 1 driveway / 35 minutes = 1/35 driveway per minute.
To find their combined work rate when they work together, we simply add their individual work rates. So, the combined work rate of Sue and Tom working together is (1/40 + 1/35) driveways per minute.
To find out how long it would take them to shovel the driveway together, we can calculate the reciprocal of their combined work rate. The reciprocal of (1/40 + 1/35) is 35 * 40 / (35 + 40) = 1400 / 75 = 18.67 minutes.
Therefore, it would take Sue and Tom approximately 18.67 minutes to shovel the driveway together.