if jack can mow his lawn in 4 hours and sue can mow the same lawn in 7 hrs how much time if they both mowed the lawn together???
Jack's rate = 1/4
Sue's rte = 1/7
combined rate = 1/4 + 1/7 = 11/28
combined time = 1/(11/28) = 28/11 = 2.5454..
or 2 hrs, 33 minutes (appr for minutes)
Thanks for showing me.
To find out how much time it would take for Jack and Sue to mow the lawn together, we can use the concept of work rates.
The work rate can be thought of as the amount of work done per unit of time. In this case, the work is mowing the lawn, and the unit of time is hours.
Let's say that Jack's work rate is Wj (in terms of lawn per hour) and Sue's work rate is Ws (in terms of lawn per hour).
If Jack can mow the lawn in 4 hours, then his work rate can be calculated as Wj = 1 lawn / 4 hours = 1/4 lawns per hour.
Similarly, if Sue can mow the lawn in 7 hours, her work rate can be calculated as Ws = 1 lawn / 7 hours = 1/7 lawns per hour.
To find out how much time it would take for them to mow the lawn together, we need to calculate their combined work rate.
When working together, their work rates add up. So, the combined work rate (Wc) is calculated by adding their individual work rates: Wc = Wj + Ws.
Wc = 1/4 lawns per hour + 1/7 lawns per hour.
Now, we can simplify the equation to get a common denominator:
Wc = 7/28 lawns per hour + 4/28 lawns per hour = 11/28 lawns per hour.
This means that, when working together, Jack and Sue can mow 11/28 of the lawn in one hour.
To find out how much time it would take for them to mow the entire lawn, we can set up a proportion:
(11/28 lawns / hour) = 1 lawn / X hours.
To solve for X (the time it would take for them to mow the lawn together), we can cross-multiply and divide:
11/28 = 1/X.
Cross-multiplying gives us:
11X = 28.
Dividing both sides by 11 gives us:
X = 28/11.
Therefore, when Jack and Sue mow the lawn together, it would take them approximately 2.54 hours or 2 hours and 32 minutes to finish the task.