Question

A car takes 2 hours less than a train incovering a distance of 500 km. Due to sometechnical reasons the speed of car is halved.Now it takes 2 hours more than a train tocover the same distance. Find the speed ofcar and train

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Answer 1

Answer:-

Given:

A car takes 2 hrs less than a train in covering a distance of 500 km.

Let's assume that the time taken by train to cover 500 km be x hrs.

We know that,

Speed = Distance/Time

So,

⟹ Speed of the train = (500/x) km/hr

Time taken by the car is 2hrs less than that of train.

so,

⟹ Time taken by car to cover 500 km = (x - 2) hrs.

Also,

⟹ Speed of the car = ( 500/x - 2) km/hr

It is also given that,

Due to some technical reasons, the speed of the car is halved and it takes 2 hrs more than time taken by the train to cover the same distance.

So, according to the above condition,

• New speed of car = 1/2 [ 500/x - 2 ] km/hr

• Time taken = (x + 2) hrs.

• Distance = 500 km

We know that,

Distance = speed * time

So,

⟹ 500 = New speed of car * Time taken

⟹ 500 = 1/2 [ 500/x - 2 ] * (x + 2)

On cross multiplication we get,

⟹ 500 * 2 (x - 2) = 500 (x + 2)

[ 500 get cancelled both sides ]

⟹ 2x - 4 = x + 2

⟹ 2x - x = 2 + 4

⟹ x = 6

Hence, Time taken by train = x = 6 hrs

∴

• Speed of train = 500/x = 500/6 = 83.33 km/hr

• Speed of car = 500/x - 2 = 500/6 - 2 = 500/4 = 125 km/hr.

Answer 2

Step-by-step explanation:

• let the time taken by the train be x
• time taken by car= x-2 hrs
• distance = 500 km
• initial speed of car = 500/x-2 km/h

• final speed of car initial speed
• 2= (500/x-2)/2
• = 250/x-2

• time taken now = x + 2 hrs
• final speed = 500/x + 2 hrs
• 250/x-2500/x+2
• 250(x+2) = 500(x-2)
• 250x + 500 500x1000 500+1000 = 500x-250x

• time taken by train = 6 hrs
• time taken by car = x - 2 = 4hrs