- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h, it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.

Given:

A train covered a certain distance at a uniform speed. If the train could have been 10 km/hr. faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/hr; it would have taken 3 hours more than the scheduled time.

To do:

We have to find the distance covered by the train.

Solution:

Let the original speed of the train be $x$ km/hr, the distance travelled by train be $y\ km/hr$ and the time taken be $t$.

This implies,

Time taken by the train to travel $y$ km at original speed$t=\frac{y}{x}$ hours.

$\Rightarrow y=xt$....(i)

If the train could have been 10 km/hr. faster, it would have taken 2 hours less than the scheduled time.

Time taken by the train to travel $y$ km when the speed is 10 km/hr more than the original speed$=\frac{y}{x+10}$ hours

According to the question,

$\frac{y}{x+10}=t-2$

$\frac{xt}{x+10}=t-2$ (From (i))

$xt=(t-2)(x+10)$

$xt=xt+10t-2x-20$

$10t-2x-20=0$......(ii)

If the train were slower by 10 km/hr; it would have taken 3 hours more than the scheduled time.

Time taken by the train to travel $y$ km when the speed is 10 km/hr less than the original speed$=\frac{y}{x-10}$ hours

According to the question,

$\frac{y}{x-10}=t+3$

$\frac{xt}{x-10}=t+3$ (From (i))

$xt=(t+3)(x-10)$

$xt=xt-10t+3x-30$

$3x-10t-30=0$......(iii)

Adding equations (ii) and (iii), we get,

$10t-2x-20+3x-10t-30=0$

$x-50=0$

$x=50$

Substituting the value of $x=50$ in equation (iii), we get,

$3(50)-10t-30=0$

$150-10t-30=0$

$10t=120$

$t=12$

Distance covered by the train $y=xt=50(12)=600$

The distance covered by the train is $600$ km.

- Related Questions & Answers
- Have you ever been in a jail? If yes, what have you faced?
- Factors Affecting the Schedule Speed of an Electric Train
- Crest Speed, Average Speed & Schedule Speed of an Electric Train
- How to find the files in Linux that have been changed in the last 24 hours?
- Difference between Metro Train and Conventional Train
- Find the minimum cost to reach destination using a train
- Query results that have less than X characters in MySQL?
- What would be the output of MySQL SUM() function if a column having no values has been passed as its argument?
- How to subset rows of an R data frame if all columns have values greater than a certain value
- How to subset rows of an R data frame if any columns have values greater than a certain value?
- Check if any value in an R vector is greater than or less than a certain value.
- Is it necessary to have a responsive website?
- What would you do if you were made a superhero for a day?
- Execute a script when there have been changes to the anchor part of the URL in HTML?
- Find items that do not have a certain field in MongoDB?
- Why goods train has 58 wagons, passenger train has only 24 coaches?