A horse rider covers half the distance with 5 m s - 1 speed. The remaining part of the distance was travelled with speed 10 m s - 1 for half the time and with speed 15 m s - 1 for other half of the time. The mean speed of the rider averaged over the whole time of motion is x 7 m s - 1 . The value of x is ______.

Step-by-step solution

Let total distance travelled by horse rider be 2 x . Now, the time taken to cover first half distance is t A B = x 5 Second half distance x between B C is covered in two parts, x = d 1 + d 2 here d 1 is the distance travelled with 10     m   s - 1 and d 2 is the distance travelled with 15   m   s - 1 in equal time intervals t 2 each. Then, d 1 = 10 t 2 ,   d 2 = 15 t 2 Second half distance x = t 2 ( 10 + 15 ) = 25 t 2 Now, the mean speed of rider is v = 2 x x 5 + 2 x 25 = 2 × 25 5