Jay and Mark run a lawn mowing service. Mark's mower is twice as big as Jay's, so whenever they both mow, Mark mows twice as much as Jay in a given time period. When Jay and Mark are working together, it takes them 4 hours to cut the lawn of an estate. How long would it take Mark to mow the lawn by himself? How long would it take Jay to mow the lawn by himself?

Question

Jay and Mark run a lawn mowing service. Mark's mower is twice as big as Jay's, so whenever they both mow, Mark mows twice as much as Jay in a given time period. When Jay and Mark are working together, it takes them 4 hours to cut the lawn of an estate. How long would it take Mark to mow the lawn by himself? How long would it take Jay to mow the lawn by himself?

Answer 1

Let Jay's lawn mowing rate be J lawns per hour. Marks rate is 2J per lawns per hour.

To do one lawn

4 hours = 1/(J + 2J) = 1/(3J)

J = 1/12 lawn per hour

(Jay would need 12 hours to do the lawn)

Mark's rate is 1/6 lawn/hour, so one lawn would take him 6 hours.

Answer 2

It takes John 4 hours to mow a lawn. It takes Maria 3 hours to mow the same lawn. How long would it take if they worked together?

Answer 3

i don't know i want help to solve the problem solving

Answer 4

To solve this problem, let's assign some variables:

Let's say Jay's mowing rate is J lawns per hour.
Mark's mowing rate is M lawns per hour.

According to the question, Mark's mower is twice as big as Jay's, so we can conclude that Mark's mowing rate is twice as fast as Jay's. Therefore:

Mark's mowing rate, M = 2J lawns per hour.

When Jay and Mark work together, their combined mowing rate is the sum of their individual mowing rates, which means:

Jay and Mark's combined mowing rate = J + M = J + 2J = 3J lawns per hour.

We are given that when Jay and Mark work together, it takes them 4 hours to cut the lawn of an estate. This means that the lawn mowing rate (3J lawns per hour) multiplied by the time taken (4 hours) gives us the total size of the lawn:

3J * 4 = 12J lawns.

Now, we can set up two equations to solve for J and M:

Equation 1: 12J = 1 (as they together mow the entire lawn)
Equation 2: M = 2J

From Equation 1, we can isolate J by dividing both sides by 12:

J = 1/12 lawns per hour.

Now, we can substitute this value of J into Equation 2 to find M:

M = 2 * (1/12) = 1/6 lawns per hour.

Therefore, Mark can mow the entire lawn by himself in 6 hours (since his mowing rate is 1/6 lawns per hour), and Jay can mow the entire lawn by himself in 12 hours (since his mowing rate is 1/12 lawns per hour).