# A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kilometers away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is?

By Ishita Gupta|Updated : May 19th, 2023

A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kilometers away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is?

To calculate speed, one must need to know the distance traveled and the time taken. The formula for calculating speed is:

Speed = Distance / Time

It's important to ensure that the units of distance and time are consistent when calculating speed. If you are given the speed and one of the other variables (distance or time), you can rearrange the formula to solve for the missing variable.

## What is Speed?

Speed is the measure of how quickly an object moves or the rate at which it covers a certain distance in a given amount of time. It is a scalar quantity, meaning it only has magnitude and no specific direction.

Example: A runner completes a 100-meter race in 10 seconds. To calculate the speed, we divide the distance covered (100 meters) by the time taken (10 seconds). Speed = Distance / Time = 100 meters / 10 seconds = 10 meters per second. Therefore, the runner's speed is 10 meters per second.

In the above example, speed is calculated by dividing the distance traveled by the time taken. It provides information about how fast an object is moving, allowing us to compare the rates of motion of different objects.

Solution

Let's assume the speed of the car is 'x' kilometers per hour.

Since the train is 50% faster than the car, its speed can be expressed as 1.5 times the speed of the car, which is 1.5x kilometers per hour.

Now, let's calculate the time taken by the car and the train to travel from point A to point B.

For the car:

Time taken = Distance / Speed

Time taken by the car = 75 kilometers / x kilometers per hour = 75/x hours

For the train:

Time taken = Distance / Speed

Time taken by the train = 75 kilometers / (1.5x) kilometers per hour = 50/x hours

However, the train lost 12.5 minutes, which is equal to 12.5/60 hours = 0.2083 hours.

So, the actual time taken by the train would be (50/x) hours + 0.2083 hours.

Since both the car and the train reach point B at the same time, their times taken would be equal:

75/x hours = (50/x) hours + 0.2083 hours

To solve this equation, we can cross-multiply:

75 = 50 + 0.2083x

Simplifying the equation:

0.2083x = 75 - 50

0.2083x = 25

x = 25 / 0.2083

Calculating the value:

x = 120.03

Therefore, the speed of the car is approximately 120 kilometers per hour.

Summary

## A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kilometers away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is?

A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kilometers away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is 120km/hr.

Related Questions GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 help@byjusexamprep.com