Question

Ram & shyam started from a point x and y respectively and started moving towards each other. after they met ram took 4 hours to reach y and shyam took 16 hours to reach x. ram's speed is 48 kmph. what is the speed of shyam?

Answer 1

Let us say that Ram and Shyam met at point R in between X and Y after time t

Speed of Ram is given to us as 48 kmph

Let the speed of Shyam be s
If we consider the distance XR, it was covered by Ram in t hours and Shyam in 16 hours
XR distance = 48t = 16sor 3t = s or t = s/3
If we consider the distance RY, it was covered by Ram in 4 hours and Shyam in t hours


RY distance = 48*4 = st

st = 192

Putting t = s/3, we get

s(s/3) = 192

s² = 192 * 3

s² = 576

s = 24 or -24

But speed cant be negative, so s = 24

Therefore, speed of Shyam = 24 kmph

Answer 2

Let the point where Ram and Shyam be A.
Ram takes 4 hours to reach Y from A at 48 kmph. So, distance between Y and A is 48×4 = 192 kms.
Let speed of Shyam be y kmph. He takes 16 hours to reach X from A. So, the distance between X and A is 16×y = 16y kms.

So far, we have calculated:
Speed of Ram = 48 kmph
Speed of Shyam = y kmph
Distance between X and A = 16y kms.
Distance between Y and A = 192 kms.

When Ram walks from X to A, his speed is 48 kmph. So, time taken by him to reach A is 16y/48 = y/3 hours.
When Shyam walks from Y to A, his speed is y kmph. So, time taken by him to reach A is 192/y hours.

Time taken by Ram and Shyam to reach A from their initial positions should be same.
So, y/3 = 192/y → y² = 192×3 → y = √576 = 24 kmph =  speed of Shyam