You can mow your whole lawn in 45 minutes, and your neighbor can mow your whole lawn in 30 minutes. How long would it take you to mow the lawn together? Clearly show and explain each step for full credit.

Using rational applications

A. Write an equation that could be used to solve this problem.



B. Solve the equation, showing each step of your work. Find the amount of time it would take to mow the lawn together.

C. Check your work .

figure how much lawn each person can mow in one minute.

you: 1/45
neighbor: 1/30

together you can mow
1/45 + 1/30 = 2/90 + 3/90 = 5/90 = 1/18

So, you can mow it in 18 minutes together

1/x = 1/45 + 1/30

A. To solve this problem, we can set up an equation based on the concept of work. The work done by mowing the lawn can be measured in terms of time. Let's assume that the time it takes for you to mow the lawn together is represented by x.

Since you can mow the lawn in 45 minutes, your work rate is 1 lawn/45 minutes, which can be expressed as 1/45 lawns per minute. Similarly, your neighbor's work rate is 1 lawn/30 minutes, or 1/30 lawns per minute. The combined work rate of both of you mowing the lawn together is the sum of your individual work rates.

Therefore, the equation that can be used to solve this problem is:
1/45 + 1/30 = 1/x

B. To solve the equation, we need to find the LCD (Least Common Denominator) of the fractions 1/45 and 1/30, which is 90. Multiplying both sides of the equation by 90 will help get rid of the denominators:

90 * (1/45) + 90 * (1/30) = 90 * (1/x)
2 + 3 = 90/x
5 = 90/x

To isolate x, we can cross-multiply:
5x = 90

Now, divide both sides of the equation by 5 to solve for x:
x = 90/5 = 18

Therefore, it would take you and your neighbor 18 minutes to mow the lawn together.

C. To check our work, we can substitute the value of x back into the original equation and see if the equation holds true:

1/45 + 1/30 = 1/18

Let's now convert the fractions on the left side to have a common denominator of 90:

2/90 + 3/90 = 1/18
5/90 = 1/18

If we multiply both sides of the equation by 90, we get:
5 = 90/18
5 = 5

Since both sides of the equation are equal, we can conclude that our answer is correct.

Therefore, it takes 18 minutes for you and your neighbor to mow the lawn together, as explained and shown step by step.