It takes Tina 4 hours to mow a lawn herself, and Bill 5 hours to mow it himself. How long would it take to mow together?

Question

This problem is in a section about applications of rational equations and proportions.

Answer 1

Tina's rate is 1/4 of the lawn done in 1 hour

Bill's rate is 1/5 of the lawn done in 1 hour

x=# of hours it takes them working together

(1/4)(x)+(1/5)(x)=1 (job finished)

multiply both sides by 20

5x+4x=20

9x=20

x=20/9

x=2 2/9 hours working together

check:(1/4)(20/9)+(1/5)(20/9)=(5/9)+(4/9)=9/9=1 (job done)