The work is 1 yard. You want to find the time *t*.

Jeff’s rate is 1/30 and Ken’s rate is 1/45. So the combined rate is 1/30 + 1/45 .

Using the formula:

1 = ( 1/30 + 1/45 ) *t*

*t* = 18 It would take them 18 minutes to rake the yard working together.

*Review: *

There are multiple methods to deal with the fractions in work-rate equations.

*Method 1*

Multiply both sides of the equation by the LCD (least common denominator).

To find the LCD, first factor the denominators.

Then multiply each unique factor.

30 = 2 × 15

45 = 3 × 15

2 × 3 × 15 = 90

The LCD is 90.

90 = 90( 1/30 + 1/45 ) *t*

90 = ( 90/30 + 90/45 ) *t*

90 = (3 + 2) *t*

*t* = 18

*Method 2*

Factor and add fractions first.

1/30 + 1/45 = 1/2 × 15 + 1/3 × 15

= ( 3/3 ) ( 1/2 × 15 ) + ( 2/2 ) ( 1/3 × 15 )

= 3 + 2/3 × 2 × 15

= 5/3 × 2 × (3 × 5)

= 1/3 × 2 × 3

= 1/18

1 = 1/18 *t*

*t* = 18