Question

It would take Jack $4$ hours to mow the lawn if he works alone. Fortunately, after he mows for $2$ hours, Jill joins him. They finish mowing $90$ minutes later. How many minutes would it have taken for Jill to mow the entire lawn alone? Enter your answer as a number without units.

Answer 1

To find how many minutes it would have taken for Jill to mow the entire lawn alone, we need to consider the work done by Jack and Jill together. We set up an equation using their work rates and solve for Jill's work rate. Finally, we convert Jill's work rate from hours to minutes.

Step-by-step explanation:

To find out how many minutes it would have taken for Jill to mow the entire lawn alone, we need to consider the work done by Jack and Jill together. Since Jack takes 4 hours to mow the lawn alone, his work rate can be described as 1 lawn mowed in 4 hours. Let's call this rate x lawns per hour. In 2 hours, Jack would have completed 2/x of a lawn. So the remaining work that Jill and Jack completed together is 1 - 2/x. We know that they finished mowing 90 minutes (1.5 hours) after Jill joined. Considering both Jack and Jill work together for 2 hours before Jill joins, the time they both worked together is 2 + 1.5 = 3.5 hours.

Now, let's find out Jill's work rate. Let's say Jill takes y hours to mow the entire lawn alone. Her work rate can be described as 1 lawn mowed in y hours. In 3.5 hours, Jill and Jack together completed 1 - 2/x of a lawn. So, their combined work rate is (1 - 2/x) lawns per 3.5 hours. Since work rate is defined as the amount of work done per unit time, we can set up the following equation:

(1-2/x)/(3.5) = 1/y

Now we can solve this equation to find the value of y:

y = (3.5)/((1-2/x))

Simplifying this expression, we get:

y = (3.5x)/(x-2)

To find out how many minutes it would have taken for Jill to mow the entire lawn alone, we need to convert y hours to minutes:

y = (3.5x)/(x-2) * 60

Answer 2

12 hours

Step-by-step explanation:

In 1 hour jack mows 1/4 of the lawn

Together they mow half a lawn in 1.5 hours

Which is a whole lawn in 3 hours

in one hour together they mow 1/3 of the lawn

It takes Jill x hours to mow the lawn

in one hour Jill mows 1/x of the lawn

Working together in one hour

jack + jill = together

1/4 + 1/x = 1/3

1/x = 1/3 - 1/4

1/x = 4/12 - 3/12

1/x = 1/12

Cross multiply

12 = x

It takes Jill 12 hours to mow the lawn