Question

train travels 25% faster than a car. Both travels between A and B which are 120 km apart. Both start from A at the same time and reach the point B at the same time. However, train lost about 18 minutes while stopping at the stations. Find the speeds of the train and the car​

Answer 1

Given:

Let the speed of the car be v km/hr

Then the speed of the train = v + $\frac{25}{100}$v = $\frac{5}{4}$ v km/hr

Distance traveled by both car and train = 120 km

Let the time taken by the car and the train to travel 120 km be t hrs

Time lost by the train during the journey = $\frac{18}{60}$ = $\frac{3}{10}$ hrs

To Find:

Speed of the car and the train

Solution:

How is speed calculated?

• Speed is calculated as :

                            s = $\frac{distance}{time}$

• We will solve the question using the following steps:

1. Find the expression for the time taken by the car.

                        v = $\frac{120}{t}$ km/hr                      

                     ⇒ t = $\frac{120}{v}$ hrs                          (1)

2. Find the expression for the time taken by the train.

                   $\frac{5}{4}$v = $\frac{120}{\frac{13}{10}t }$ = $\frac{1200}{13t}$ km/hr              

                           ⇒ t = $\frac{960}{13v}$ hrs                (2)

3. Subtract (1) from (2) and equate the difference to the given value.

                   

                     $\frac{120}{v}$ -  $\frac{960}{13v}$ = $\frac{3}{10}$

                  ⇒ $\frac{600}{13v}$ = $\frac{3}{10}$

                  ⇒ v = $\frac{2000}{13}$

                  ⇒  v = $\frac{2000}{13}$ × $\frac{5}{18}$ ≈ 42.73 m/s   (multiplied by $\frac{5}{18}$ to convert to m/s)

Therefore, the speed of the train = $\frac{5}{4}$ × 42.73 ≈ 53.41 m/s

Hence, the speed of the car is 42.73 m/s and the speed of the train is 53.41 m/s.

Answer 2

Answer:

The speed of the car is 80 km/hr.

The speed of the train is 100 km/hr.

Step-by-step explanation:

Given distance between two points A and B is $120$km.

A train and a car start from A at the same point and reach the point B at the same time.

Also train travels 25% faster than car.

Let the speed of car be $x$ km/hr.

Then the speed of the train will be x+25% of x

$=x+\frac{25}{100}x$

$=1.25x$

Time taken taken by car should be more than time taken by the train because the speed of train is higher than the speed of the car.

But it is given train lost about 18 min while stopping at stations.

So time taken by car - 18 min = time taken by train.

We know, $Speed = \frac{Distance}{Time}$.

$Time = \frac{Distance}{Speed}$

Time taken by car = $\frac{120}{x}$

Time taken by train = $\frac{120}{1.25x}=\frac{96}{x}$

Wastage time = $18 min=\frac{18}{60}hr$

$\frac{120}{x}-\frac{18}{60}=\frac{96}{x}$

$-\frac{18}{60}=\frac{96}{x}-\frac{120}{x}$

$-\frac{3}{10}=-\frac{24}{x}$

$x=80$

The speed of the car is 80 km/hr.

$1.25x=1.25\times 80=100$

The speed of the train is 100 km/hr.