A man travels from A to B at a speed x km/hr. He then rests at B for x hours

A man travels from A to B at a speed x km/hr. He then rests at B for x hours. He then travels from B to C at a speed 2x km/hr and rests for 2x hours. He moves further to D at a speed twice as that between B and C. He thus reaches D in 16 hr. If distances A-B, B-C and C-D are all equal to 12 km, the time for which he rested at B could be

  1. 2 hr
  2. 3 hr
  3. 4 hr
  4. 6 hr

Answer

Total time taken by the man to travel from A to D = 16 hr and total distance traveled = 36 km.

The time that he would have taken had he not rested in between will be (16-x-2x) = (16-3x).

But, this time should be equal to the addition of the times that he takes to travel individual segments. This is given as:

12/x + 12/2x + 12/4x = 21/x

Therefore, 21/x = 16-3x

x = 3 or 7/3

The correct option is B.