Manhatta advanced Quant

[theachiever]

Truck A is on a straight highway heading due south at the same time Truck B is on a different straight highway heading due east. At 1:00PM, Truck A is exactly 14 miles north of Truck B.If both trucks are travelling at a constant speed of 30 miles per hour,at which of the following times will they be exactly 10 miles apart?

• A.1:10PM
  B.1:12PM
  C.1:14PM
  D.1:15PM
  E.1:20PM

[puneetkhurana2000]

Answer is B.

After 1:00 PM, truck B will be moving away from Truck A and towards east, so they will form a right angle triangle with sides 6, 8, 10. (As we have to find the time when they are 10 miles apart).

Both have same speed, so cover same amount of distance in same time.

They will cover 6 miles in 12 minutes. (30/60 * 12).

So the Right angle triangle will be like
6..horizontal distance covered by B
8..vertical distance to be covered by A (14 -6)
10 ...the distance between them.

Answer is B.

[The Iceman]

By symmetry there will be two instants when they will be exactly 10 miles apart. Both will be the case when 6-8-10 right angled triangle will be formed.

The first when each travels 6 miles and the second when each travels 8 kms.

Hence two possible instants are 1:00 + 6*60/30 and 1:00 + 8*60/30 or 1:12 PM and 1:16 PM.

Of the two the former is present in the options. Hence option B is the right choice

PS: The problem would have been funnier (read trickier) if it had been a DS problem as there are two possibilities and the info is not sufficient to uniquely determine one instant of time.