Jenny can shovel snow from her driveway in 60 minutes. Tom can do the same job in 55 minutes. How long would it take both of them together to shovel the drivway if they worked together.
I am coming up with 28 minutes.. is this correct or is it in fraction form?
T = (60 * 55) /(60 + 55) = 28.7 min.
To determine how long it would take both Jenny and Tom to shovel the driveway together, we can use the concept of "work rates."
Jenny's work rate is 1 driveway per 60 minutes, which means she can shovel the entire driveway on her own in 60 minutes.
Tom's work rate is 1 driveway per 55 minutes, which means he can shovel the entire driveway on his own in 55 minutes.
To find the combined work rate of Jenny and Tom, we can add their individual work rates. So, the combined work rate would be:
Jenny's work rate + Tom's work rate = 1/60 + 1/55
To add these fractions, we need to find a common denominator. In this case, the least common multiple (LCM) of 60 and 55 is 330.
Thus, we convert the fractions to have a common denominator of 330:
(1/60) * (55/55) + (1/55) * (60/60) = 55/330 + 60/330 = 115/330
Now that the fractions have the same denominator, we can add them:
115/330 = 23/66
This means that together, Jenny and Tom can shovel 23/66 of the driveway per minute.
To find out how long it would take them to shovel the entire driveway, we can use the concept of work = rate × time. Rearranging the formula, we have:
time = work / rate
In this case, the work is 1 (the entire driveway) and the rate is 23/66 (the combined work rate). Plugging these values into the formula:
time = 1 / (23/66) = 66/23
So, it would take Jenny and Tom approximately 66/23 minutes (about 2.87 minutes) to shovel the driveway together.