Let us assume that the distance travelled by Jim to meet John = X miles
Then the distance travelled by John to meet Jim = (3 - X) miles
We already know the equation
Time = Distance travelled/ Speed
Then for Jim,
Time = X/4
For John
Time = (3 - X)/5
As they meet, so they must have travelled the same amount of time.
Then
X/4 = (3 -X)/5
X = (12-4X)/5
5X = 12 - 4X
9X = 12
X = 12/9
= 4/3
= 1.33 miles
Now our target is to find the amount of time after which Jim and John meet.
Then
Time = X/4
= 1.33/4
= 0.33325 hours
= (0.33325 * 60) minutes
= 19.995 minutes.
So it can be safely assumed that Jim and John will meet after a period of 20 minutes.