Question

Sam can mow a lawn in 30 minutes. Rocky can mow the same lawn in 90 minutes. How long does it take for both Sam and Rocky to mow the lawn if they are working together? Express your answer as a reduced fraction.

Answer 1

Answer:

$\frac{45}{2} \ minutes$

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 = $\frac{1}{30}\ lawn$

For Rocky

Rocky can mow in 90 minutes =  1 lawn

Rocky can mow in 1 minutes = $\frac{1}{90} \ lawn$

In a case of working together:

In 1 minute, both will mow   =  $\frac{1}{30}\ lawn$ + $\frac{1}{90} \ lawn$

                                             = $\frac{3+1}{90} = \frac{4}{90} \ lawn$

To mow $\frac{4}{90} \ lawn$ together, it takes = 1 minute

So, to mow 1 lawn together, it takes = $\frac{1}{\frac{4}{90} } =\frac{90}{4} =\frac{45}{2} \ minutes$

Thus, both Sam and Rocky will mow the lawn together in $\frac{45}{2} \ minutes$