Lisa can shovel snow from her driveway in 45 minutes. Bill can do the same job in 65 minutes. How long would it take Lisa and Bill to shovel the driveway if they worked together?
Each minute, Lisa will shovel 1/45 of the driveway, while Bill will shovel 1/65 of the driveway.
Together, each minute they will shovel
(1/45+1/65) of the driveway.
They will take
1/(1/45+1/65) minutes to shovel the whole driveway.
Note: the answer is between 26 and 27 minutes.
2.5
To find out how long it would take Lisa and Bill to shovel the driveway if they worked together, you can use the concept of work rates. The work rate is the amount of work done per unit of time.
Let's calculate the work rate of Lisa and Bill individually:
- Lisa can shovel the entire driveway in 45 minutes, so her work rate is 1/45 of the driveway per minute.
- Bill can shovel the entire driveway in 65 minutes, so his work rate is 1/65 of the driveway per minute.
To find their combined work rate, you add up their individual work rates:
1/45 + 1/65
Next, you want to find the time it would take for them to complete the job together. Let's call this time "t."
The formula for work rate is work rate = work / time.
Since Lisa and Bill are shoveling the same driveway, their work is the same, which means their combined work rate multiplied by the time it takes (t) should be equal to 1 (representing the whole driveway):
(1/45 + 1/65) * t = 1
Now we can solve this equation to find the value of t, which represents the time it would take for Lisa and Bill to shovel the driveway together.