## Question

###### 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 ?

## Answers

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