Question

Two persons A & B travelling towards each other from P & Q respectively
which is 396 kms apart meet after 11 hours. Speed of A is 6 kms/hr more than B.
Find the speed of B.

Answer 1

Explanation:

Let person A travel from point P towards point Q 396 km apart at a speed = u km/h. At the same time as A starts his travel from point P towards Q, another person B starts to travel from point Q towards point P with a speed (u —6) km/h. The persons A and B, meet each other after 11hour at some point in between the points P and Q.

The relative speed of A with respect B can be found by imposing on person B a speed of (u —6) directed along PQ. The imposition of the speed (u —6) along PQ would bring B to stand still as the imposed speed is equal and opposite to its original speed (u —6) along QP. We need to impose the same speed (u — 6) along PQ also on A which was already moving with a speed u along PQ. The effective speed of A becomes (u +u —6) km/h = (2 u — 6) km/h.

Travelling at an effective speed of (2u — 6) km/h the distance between PQ is covered in 11 hour, that is

396/(2u — 6) = 11

=> 11(2u — 6) = 396

=> (2 u — 6) = 36

=> 2 u = 36 + 6 = 42

=> u = 21 km/h

So person A travels at a speed of 21 km/h and person B travel at a speed of (21 — 6) = 15 km/h. In 11 hours person A travels a distance = (21 km/h) × 11 h = 231 km from pont P towards Q and person B travels a distance = (15 km/h) × 11 hour = 165 km from point Q towards point P. Total distance travelled by persons A and B = 231 km + 165 km = 396 km.

Answer 2

Given : d = 396 km ; time of travel = 11 h ; speed_A = v + 6 ; speed_B = v

What is the speed of B?

This can be answered by the equation (v + v + 6) * 11 = 396

Solving for the speed of B which is designated as v

(speed_A + speed_B) * 11 h = 396 km

(v + 6 + v) * 11 = 396

(2v + 6) * 11 = 396

22v + 66 = 396

22v = 396 - 66

22v = 330

v = 330 ➗ 22

v = 15 km per hour

The speed of B is 15 km per hour. It follows that the speed of A is 21 km per hour. The combined speed is 36 km per hour. Multiply 36 km/h by 11 h and we get a distance traveled of 396 km.