Question

A motorcycle travels 20 km an hour faster than a cycle over a journey of 600 km. The cycle takes 15 hours more than the motorcycle. Find the speed of the motorcycle.

Answer 1

Let the cycle speed X then motorcycle speed will be X + 20.

600/X - 600/(X+20) = 15.

X = 20 i.e cycle speed.

Motorcycle speed = 20 + 20 = 40.

Answer 2

Answer:

40 km/h

Step-by-step explanation:

Let x km/h be the speed of cycle,

⇒ Speed of motorcycle = (x+20) km/h,

Total distance = 600 km,

Since, Time = Distance / Speed,

Also, The cycle takes 15 hours more than the motorcycle,

⇒ $\frac{600}{x}-\frac{600}{x+20}=15$

$600(\frac{1}{x}-\frac{1}{x+20})=15$

$\frac{x+20-x}{x(x+20)}=\frac{15}{600}$

$\frac{20}{x(x+20)}=\frac{1}{40}$

$800=x(x+20)$       ( By cross multiplication )

$\implies x^2+20x-800=0$  

By solving this quadratic equation,

We get,

x = 20  or - 40

But speed can not be negative,

Thus, the speed of the motorcycle = x + 20 = 20 + 20 = 40 km/h