Question

1. A train covers 120 km at a uniform speed.
If its speed had been increased by 15 km/h,
it would have covered the distance in 40
minutes less. Find the original speed.

Answer 1

Answer:

Refer the attachment

*Correction : Its (3/x) - [3/(x+15)] = 1/60

Step-by-step explanation:

Answer 2

Given,

Distance covered by a train at a uniform speed = 120 Km

If its speed had been increased by 15 km/h,

it would have covered the distance in 40

minutes less.

To find,

The original speed of the train.

Solution,

We can simply solve this numerical problem by using the following process:

Let us assume that the original speed of the train is x Km/hr.

Mathematically,

speed (s) = distance traveled (d)/time of journey(t)

=> time of journey(t) = distance traveled (d)/speed (s)

{Statement-1}

Now, according to the question:

When the train covered 120 km at a uniform original speed, the time taken to complete the journey

= distance traveled (d)/speed (s)

{according to statement-1}

= (120 Km)/(x Km/hr)

= (120/x) hr

Also, according to the question;

When the train covered 120 km at a speed increased by 15 Km/hr, the time taken to complete the journey

= distance traveled (d)/speed (s)

{according to statement-1}

= (120 Km)/(x+15) Km/hr

= 120/(x+15) hr

Now, according to the question;

(the time taken to complete the journey when the train covered 120 km at a uniform original speed) = 40 minutes + (the time taken to complete the journey when the train covered 120 km at a speed increased by 15 Km/hr)

=> (120/x) hr = (40/60) hr + 120/(x+15) hr

=> 120/x - 120/(x+15) = 2/3

=> 1/x - 1/(x+15) = 2/(3×120) = 1/180

=> {(x+15) - x}/x(x+15) = 1/180

=> 15/x(x+15) = 1/180

=> x(x+15) = 15×180

=> x^2 + 15x - 2700 = 0

=> x^2 + 60x - 45x - 2700 = 0

=> x(x+60) - 45(x+60) = 0

=> (x+60)(x-45) = 0

=> (x+60) = 0 or (x-45) = 0

=> x = -60 Km/hr or x = 45 Km/hr

But speed can never be a negative quantity.

=> the original speed of the train is 45 Km/hr

Hence, the original speed of the train is 45 Km/hr.