Problem 1.

Working together, Rick and Juanita can complete a job in 6 hrs. It would take Rick 9 hrs longer thank Juanita to do the job alone. How long would it take Juanita alone?

j = the number of hours Juanita needs to do the job alone, j>0

j + 9 = the number of hours Rick need to do the job alone

6 hr the need to complete the job together

1/j + 1/(j + 9) = 1/6

by solving we find

j = 9 hours

click here to see the step by step solution of the equation

Juanita needs 9 hours to finish the job alone.

Problem 2.

A rectangle has a area of 12ft x 5 ft. A gravel path equal width is to be built around the garden. How wide can the path be if there is enough gravel for 138 sq. ft.?

w = the width of the gravel path

(12 + 2w)(5 + 2w) - 12*5 = 138

by solving we find

w = 3 ft

click here to see the step by step solution of the equation

the path can be 3 feet wide.