# 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 ___ km/hr.

Calculate the original speed of a train traversing 480 km, encountering a hypothetical scenario where a slight speed reduction results in 3 additional hours of travel time. Dive into the solution now!

by Maivizhi A

**Updated **Mar 06, 2024

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## 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 ___ km/hr.

The original speed of the train is 40 km/hr.

Let's denote the original speed of the train as S km/hr.

According to the given information:

- When traveling at the original speed, the time taken to cover 480 km is 480/S hours.
- When traveling at a speed 8 km/hr less than the original speed, the time taken to cover the same distance is 480/(S-8) hours.

It's given that the difference in time taken is 3 hours. So, we can set up the equation:

480/S - 480/(S-8) = 3

Now, let's solve this equation to find the value of S:

(480(S-8) - 480S) / (S(S-8)) = 3

(-3840) / (S^2 - 8S) = 3

-3840 = 3S^2 - 24S

3S^2 - 24S - 3840 = 0

Now, we'll solve this quadratic equation using the quadratic formula:

S = (-b ± √(b^2 - 4ac)) / (2a)

Where: a = 3, b = -24, c = -3840

S = (24 ± √(576 + 46080)) / 6

S = (24 ± √46656) / 6

S = (24 ± 216) / 6

Now, we have two possible values for S:

- S1 = (24 + 216) / 6 = 240/6 = 40 km/hr
- S2 = (24 - 216) / 6 = -192/6 = -32 km/hr

Since the speed cannot be negative, we discard S2.

Therefore, the original speed of the train is 40 km/hr.

## Speed, Distance and Time in Mathematics

Speed, distance, and time are interconnected concepts in mathematics and physics. They are often used together to solve problems involving motion. Here's a breakdown of each concept:

- Speed: Speed is the rate at which an object covers distance. It is defined as the distance traveled per unit of time. Mathematically, speed is expressed as:
Speed = Distance / Time

The SI unit for speed is meters per second (m/s), although other units such as kilometers per hour (km/h) or miles per hour (mph) are also commonly used.

- Distance: Distance is the total length of the path covered by an object in motion. It is measured in units such as meters, kilometers, miles, etc.
- Time: Time is the duration of the motion or the period during which an object is in motion. It is measured in units such as seconds, minutes, hours, etc.

When solving problems involving speed, distance, and time, you can use the following formulas:

- To find speed:
Speed = Distance / Time

- To find distance:
Distance = Speed × Time

- To find time:
Time = Distance / Speed

It's important to pay attention to the units used for each variable and ensure they are consistent throughout the problem. If units are different, conversions may be necessary to maintain consistency.

Here are a few examples of problems involving speed, distance, and time:

- If a car travels at a constant speed of 60 km/h, how far will it travel in 3 hours? Solution: Distance = Speed × Time = 60 km/h × 3 hours = 180 km
- A cyclist covers a distance of 45 kilometers in 2 hours. What is their average speed? Solution: Speed = Distance / Time = 45 km / 2 hours = 22.5 km/h
- A train travels a distance of 300 miles at a speed of 50 miles per hour. How long does it take for the train to complete its journey? Solution: Time = Distance / Speed = 300 miles / 50 mph = 6 hours

These examples demonstrate how speed, distance, and time are related and how they can be used to solve various problems involving motion.

## 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 - FAQs

### 1. What is the problem statement regarding the train's journey?

The problem states that a train travels a distance of 480 km at a uniform speed. If its speed were 8 km/hr less, it would take 3 hours more to cover the same distance.

### 2. How do we denote the original speed of the train?

The original speed of the train is denoted as 'S' km/hr.

### 3. What equation represents the time difference between the two scenarios?

The equation representing the time difference is: 480/S - 480/(S-8) = 3.

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