Answer:
6 hours
Explanation:
Let's assume that Jack can mow the lawn at a rate of x units per hour, and Mary can mow the same lawn at a rate of y units per hour.
Then, we have:
Amount of work done by Jack in 1 hour = x units/hour x 7 hours = 7x units
Amount of work done by Mary in 1 hour = y units/hour x 5 hours = 5y units
Amount of work done by Jack and Mary in 1 hour = (x + y) units/hour
Now, we can set up the equation:
7x + 5y = (x + y)t
where t is the time taken by Jack and Mary to mow the lawn together.
Simplifying this equation, we get:
6x = yt
Dividing both sides by 6y, we get:
x/y = t/6
This equation tells us that the ratio of Jack's rate to Mary's rate is equal to the ratio of the time Jack and Mary took to mow the lawn together to 6 hours.