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 BYJU'S Exam Prep
Updated on: September 25th, 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.
Table of content
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
- What Are The First 30 Elements
- Write Five Uses Of Convex Mirror
- Find five rational numbers between 3/5 and 4/5
- In Indian rupees, 1 trillion is equal to how many crores?
- Find the Probability of a Leap Year having 53 Sundays
- A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/hr less, then it would have taken 3 hours more to cover the same distance. The original speed of the train is
- A and B invest in a business in the ratio 3: 2. If 5% of the total profit goes to charity and A’s share is Rs.855, the total profit is
