Answer:
![\frac{45}{2} \ minutes](https://tex.z-dn.net/?f=%5Cfrac%7B45%7D%7B2%7D%20%5C%20minutes)
Step-by-step explanation:
Given:
Sam can mow a lawn in 30 minutes.
Rocky can mow the same lawn in 90 minutes.
Question asked:
How long does it take for both Sam and Rocky to mow the lawn if they are working together?
Solution:
By unitary method:
<u>For Sam</u>
Sam can mow in 30 minutes = 1 lawn
Sam can mow in 1 minute = ![\frac{1}{30}\ lawn](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B30%7D%5C%20lawn)
<u>For Rocky</u>
Rocky can mow in 90 minutes = 1 lawn
Rocky can mow in 1 minutes = ![\frac{1}{90} \ lawn](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B90%7D%20%5C%20lawn)
In a case of working together:
In 1 minute, both will mow =
+
= ![\frac{3+1}{90} = \frac{4}{90} \ lawn](https://tex.z-dn.net/?f=%5Cfrac%7B3%2B1%7D%7B90%7D%20%3D%20%5Cfrac%7B4%7D%7B90%7D%20%5C%20lawn)
To mow
together, it takes = 1 minute
So, to mow 1 lawn together, it takes = ![\frac{1}{\frac{4}{90} } =\frac{90}{4} =\frac{45}{2} \ minutes](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Cfrac%7B4%7D%7B90%7D%20%7D%20%3D%5Cfrac%7B90%7D%7B4%7D%20%3D%5Cfrac%7B45%7D%7B2%7D%20%5C%20minutes)
Thus, both Sam and Rocky will mow the lawn together in