Question

a cycle covers a distance of 60 km in a direction of wind and come back in his original position in 8 hours if the speed of the wind is 10 km per hour find the speed of bicycle

Answer 1

Answer:Let the speed of bicycle be x km / hr

Speed of wind is 10 km /hr

Speed of bicycle in the direction of wind = (x + 10) km/hr

Speed of the bicycle against the direction of wind = (x – 10) km/hr

Speed = Distance / Time

Time = Distance / Speed

Time taken by man when riding in the direction of wind = (60 / x+10) hrs

Time taken by man when riding the opposite direction of wind= (60 / x-10) hrs

(60 / x +10)  + (60 / x+10) = 860[(1 / x+10) + (1 / x-10)] = 8

[(1 / x+10) + (1 / x-10)] = 8/60

2x / x2 - 100 = 2 / 15

⇒ x2 - 15x - 100 = 0

⇒ (x + 5)(x - 20) = 0

⇒ x = -5 or 20

Speed can never be negative. Hence x = 20.

Therefore, the speed of the bicycle is 20km/hr