John and Jim can finish a job in 2 hours working together. it takes John 3 hours less then Jim to finish the job alone. number of hours each to finish job?

Question

I need help on creating and solving an equation for this word problem. 

Answer 1

Let x = the number of hours it takes John to finish the job alone, and y = the number of hours its takes Jim to finish the job alone.

 

The rate at which John works is 1/x (1 job in x hours); the rate at which Jim works is 1/y (1 job in y hours).

 

If they work together and can finish the job in 2 hours, then the equation

 

2/x + 2/y = 1 applies.

 

Since you also know that x = y - 3 (John's time is three less than Jim's time), you have a system of two equations in x and y.

 

You can solve this by replacing y by x + 3 in the first equation and solving for x, then plug in this number into y = x + 3 to find y.

 

Let me know if you need more explanation for solving this equation.