Question

A train travels a distance of 120 km at a constant speed of V kmh 1. If the speed

is reduced by 10kmh), then the time taken to the journey is increased by one
hour. Find the constant speed V of train.


Help me please

Answer 1

V = 40 km/h

Explanation:

Total distance = 120 km

Constant speed of train = V km/h

⇒
`Time \: taken \: by \: train = (Distance)/(Speed) = (120)/(V) \: hr`

Its given that if speed is reduced by 10 km/h , the time taken by train increases by 1 hour. BUT THE DISTANCE REMAINS SAME. So,

`Speed * Time = Distance`

`=> (V - 10)((120)/(V) + 1) = 120`

`=> 120 + V - (1200)/(V) - 10 = 120`

`=> V - (1200)/(V) - 10 = 0`

`=> (V^2 - 1200 - 10V)/(V) = 0`

`=> V^2 - 10V - 1200 = 0`

Factorise the quadratic equation.

`=> V^2 - 40V + 30V - 1200`

`=> V(V - 40) + 30(V - 40)`

`=> (V - 40)(V + 30)`

`=> V = 40 \: (or) \: -30`

Speed can't be negative. So , V = 40 km/h