# On a 120 km track, A train travels the first 30 km at a uniform speed of 30km/h. Calculate the speed with which the train should move the rest of the track so as to get the average speed of 60km/h for the entire trip.

Find the speed needed for a train to maintain an average speed of 60km/h over a 120 km journey, given it travels the first 30 km at 30km/h.

by Maivizhi A

**Updated **Mar 06, 2024

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## On a 120 km track, A train travels the first 30 km at a uniform speed of 30km/h. Calculate the speed with which the train should move the rest of the track so as to get the average speed of 60km/h for the entire trip.

The speed at which the train should move the rest of the track is 90 km/h.

To find the speed at which the train should move the rest of the track to achieve an average speed of 60 km/h for the entire trip, we can use the formula for average speed:

Average Speed = Total Distance / Total Time

Given that the train travels 30 km at a speed of 30 km/h, it takes 1 hour to cover this distance.

Now, let's denote the speed at which the train should move the remaining distance as "v" km/h.

The remaining distance is 120 - 30 = 90 km.

To find the time it takes to cover this distance at speed "v", we use the formula:

Time = Distance / Speed

So, the time taken to cover the remaining distance is:

Time = 90 / v

Now, the total time for the entire trip is the sum of the time taken for the first part (30 km) and the time taken for the remaining part (90 km):

Total Time = 1 + 90 / v

We want the average speed to be 60 km/h, so we set up the equation:

60 = 120 / (1 + 90 / v)

To solve for "v", we first multiply both sides by (1 + 90 / v):

60(1 + 90 / v) = 120

60 + 5400 / v = 120

Subtracting 60 from both sides gives:

5400 / v = 60

Now, to isolate "v", we divide both sides by 60:

5400 / (60v) = 1

90 = v

So, the speed at which the train should move the rest of the track is 90 km/h.

## Speed, Time and Distance in Mathematics

Speed, time, and distance are fundamental concepts in mathematics and physics that are often interrelated. Here's an overview of how they relate to each other:

Speed: Speed is defined as the rate at which an object covers distance. Mathematically, speed is calculated as the distance traveled divided by the time taken to travel that distance. The standard unit for speed is distance per unit time, such as meters per second (m/s) or kilometers per hour (km/h).

Speed = Distance / Time

Time: Time is the duration during which an event occurs or an object moves from one position to another. It is measured in units such as seconds, minutes, hours, etc.

Distance: Distance is the measure of how far an object has moved. It is usually measured in units such as meters, kilometers, miles, etc.

The relationship between speed, time, and distance can be summarized by the formula:

Distance = Speed × Time

This formula can be rearranged to find any of the three variables given the other two. For example:

If you know the speed and the time, you can find the distance traveled.

If you know the distance and the time, you can find the speed.

If you know the distance and the speed, you can find the time taken.

Here are some common scenarios where these concepts are applied:

Constant Speed: When an object moves at a constant speed, the distance it covers is directly proportional to the time it takes. So, if the speed is constant, you can calculate the distance by multiplying the speed by the time.

Varying Speed: If the speed of an object is not constant, you may need calculus to determine the distance traveled over a given time interval.

Relative Speed: When two objects are moving relative to each other, their speeds can be combined or subtracted to find their relative speed.

Average Speed: If an object travels at different speeds during a journey, its average speed over the entire journey can be calculated by dividing the total distance traveled by the total time taken.

These concepts are used extensively in various fields such as physics, engineering, navigation, and everyday activities like commuting, sports, and transportation planning. Understanding the relationships between speed, time, and distance is essential for solving many real-world problems

## On a 120 km track, A train travels the first 30 km at a uniform speed of 30km/h. Calculate the speed with which the train should move the rest of the track.. - FAQs

### 1. What is the primary formula used to calculate average speed?

The primary formula for average speed is: Average Speed = Total Distance / Total Time.

### 2. How is time calculated in the context of speed and distance?

Time is calculated using the formula: Time = Distance / Speed.

### 3. What are the initial conditions given for the train's journey on the 120 km track?

The train travels the first 30 km at a uniform speed of 30 km/h.

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