One hour before John started walking from P to Q, a distance

This is again a relative speed question and I would suggest you to check out the links given in my previous post.


Ann walks from Q to P at a speed of 3 miles/hr for one hour. She covers 3 miles in 1 hour and now distance between John and Ann is 18 - 3 = 15 miles.

Ann walks at 3 mph and John at 2 mph so their relative speed is 3+2 = 5 mph.

They have to cover 15 miles so it will take them 15/5 = 3 hours to meet.
In 3 hrs, Ann would have covered 3 hrs * 3 miles per hour = 9 miles.

Adding this to the 3 miles she covered before John, Ann covered a total of 3 + 9 = 12 miles.

Answer (E)

Another Method:
You can also use ratios to say that Ann and John have 15 miles between them (after Ann covers 3 miles) and their speeds are in the ratio 3:2. So Ann will cover 3/5 of the distance i.e. (3/5)*15 = 9 miles.
This gives a total distance of 3 + 9 = 12 miles