Ron can deliver papers 8 hours faster than jimmy . But together they deliver papers in 3 hours. write an equation on how long it takes jimmy

Question

Algebra 2

Answer 1

Let J = # hours it takes Jimmy to deliver papers

J-8 = # hours it takes Ron to deliver papers.

Together they can deliver papers in 3 hours

 

1/J + 1/(J-8) = 1/3

 

Now let's solve.  The common denominator is 3J(J-8).

 

3(J-8) +3J       J(J-8)

------------  =  ------

  3J(J-8)         3J(J-8)

 

Since the denominators are the same on both sides, in order for the equation to balance, we need to make the numerators equal.

 

So,

3(J-8) + 3J = J(J-8)

3J - 24 + 3J = J² - 8J

 

Rearrange the terms

0 = J² - 14J + 24

0 = (J - 2) (J - 12)

 

So J = 2 or 12.

But J=2 does not makes sense.  Since Ron delivers papers 8 hours faster than Jimmy, if J=2, then Ron would deliver papers in -6 hours.

 

So the solution is Jimmy delivers papers in 12 hours and Ron delivers papers in 4 hours.