I can grade these quizzes in 2 hours. My wife can grade them in 5 hours. How long will it take us to grade them if we work together

Question

Professor in college asked us this question. And his wife teaches 5th grade 

Answer 1

This is a classic work problem and it is always difficult to justify the way it works.

 

1/5 + 1/2 = 1/x => x = 10/7

 

You can think of it this way:

 

The husband's rate is Job/2 hr; the wife's rare is Job/5 hrs.

Let x be the total hours spent working together.

 

(Job/5)x + (Job/2)x  = Job

Divide through by Job and then by x to get the equation I started with.

 

In other problems Job might be square feet painted, then square feet painted/2 is square feet per hour which is then multiplied by hours to get square feet..