Answer:
[tex]\frac{45}{2} \ minutes[/tex]
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:
For Sam
Sam can mow in 30 minutes = 1 lawn
Sam can mow in 1 minute = [tex]\frac{1}{30}\ lawn[/tex]
For Rocky
Rocky can mow in 90 minutes = 1 lawn
Rocky can mow in 1 minutes = [tex]\frac{1}{90} \ lawn[/tex]
In a case of working together:
In 1 minute, both will mow = [tex]\frac{1}{30}\ lawn[/tex] + [tex]\frac{1}{90} \ lawn[/tex]
= [tex]\frac{3+1}{90} = \frac{4}{90} \ lawn[/tex]
To mow [tex]\frac{4}{90} \ lawn[/tex] together, it takes = 1 minute
So, to mow 1 lawn together, it takes = [tex]\frac{1}{\frac{4}{90} } =\frac{90}{4} =\frac{45}{2} \ minutes[/tex]
Thus, both Sam and Rocky will mow the lawn together in [tex]\frac{45}{2} \ minutes[/tex]
