Murphy and Belle run along a road, starting 500 meters away from each other. If they run in opposite directions, how long does it take for them to be 5000 m away from each other, given that Murphy runs at 200 m per minute and Belle runs at 300 m per min ?

It takes #9# minutes for them to be #5000# meters away from each other.

Explanation:

You can solve this problem with logic.

Every minute they run, they increase the distance between themselves by 500 meters.

#200# m#larr##"---------|-----------"# #rarr# #300# m
#color(white)(...............)#( #color(white)()# #larr# #500# m#rarr#)

When they begin, they are already #500# meters apart, so they have to add #4500# meters additional to become #5000# m apart.

They add #500# meters more each minute, so they need #9# minutes to add #4500# additional meters and become #5000# meters apart

Check
#9# minutes @ #200# m per minute . . . #1800# m #larr# Murphy
#9# minutes @ #300# m per minute. . . .#2700# m #larr# Belle
Distance apart at the start . . . . .. . . .#500# m
...................................................................................................
Distance apart after #9# minutes . . . .#5000# m

#Check#

9 minutes.

Explanation:

Distance = Rate * Time

5000 - 500 = 4500 m => distance to go

Since they are running in opposite direction their speed can be combined:

Rate = 300 + 200 = 500 mpm

Time = Distance/Rate

Time = 4500/500 = 9 minutes