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

Answer:

V = 40 km/h

Step-by-step explanation:

Total distance = 120 km

Constant speed of train = V km/h

⇒ $Time \: taken \: by \: train = \frac{Distance}{Speed} = \frac{120}{V} \: hr$

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,

$Speed \times Time = Distance$

$=> (V - 10)(\frac{120}{V} + 1) = 120$

$=> 120 + V - \frac{1200}{V} - 10 = 120$

$=> V - \frac{1200}{V} - 10 = 0$

$=> \frac{V^2 - 1200 - 10V}{V} = 0$

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

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