Jeff and Bianca are proofing articles for the school newspaper. Bianca works one and a half times as fast as Jeff. Together they edit 2500 words in 3 hours. How long does it take each editor working alone, to edit a 2500-word newspaper?

Jeff=7.5 hrs

Bianca=5 hrs

Step-by-step explanation:

First you need to find how many words they each edited, so make x=words edited. Bianca edits 1.5 times as many words than Jeff (per hour) so the equation can be written as x (words Jeff edited) + 1.5x (words Bianca edited) = 2500. So 2.5x=2500, so x=1000 (Jeff's words edited), so if you multiply by 1.5 you get Bianca's words edited of 1500. However all of this happened over 3 hours so to get their words per hour divide their total words (what we just found) by 3 to get

Jeff = 333.3 words per hour

Bianca = 500 words per hour

Now define y=hours, and to find the hours to edit 2500 words set the equation of words per hour times hour equal to 2500 words, and you can make two equations:

Jeff 333y=2500

Bianca 500y=2500

Solve for both of those and you get:

Jeff = 7.5 hrs

Bianca = 5 hrs