# a train covered a certain distance at a uniform speed. if the train would have been 6 km/h faster, it would have taken 4 hours less than the scheduled time. and, if the train were slower by 6 km/hr ; it would have taken 6 hours more than the scheduled time. find the length of the journey.

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get a train covered a certain distance at a uniform speed. if the train would have been 6 km/h faster, it would have taken 4 hours less than the scheduled time. and, if the train were slower by 6 km/hr ; it would have taken 6 hours more than the scheduled time. find the length of the journey. from screen.

## A train covered a certain distance at a uniform speed. If the train would have been 6 km/h faster, it would have taken 4 hours less than the scheduled time. And, if the train were slower by 6 km/h, it would have taken 6 hours more than the scheduled time. Find the length of the journey.

Click here👆to get an answer to your question ✍️ A train covered a certain distance at a uniform speed. If the train would have been 6 km/h faster, it would have taken 4 hours less than the scheduled time. And, if the train were slower by 6 km/h, it would have taken 6 hours more than the scheduled time. Find the length of the journey.

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## A train covered a certain distance at a uniform speed. If the train would have been 6 km/h faster, it would have taken 4 hours less than the scheduled time. And, if the train were slower by 6 km/h, it would have taken 6 hours more than the scheduled time. Find the length of the journey.

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Updated on : 2022-09-05

Let the actual speed of the train be x km/hr and the actual time taken be y hours. Then,Solution Verified by Toppr

Distance covered =(xy)km ..(i) [∴ Distance = Speed × Time]

If the speed is increased by 6 km/hr, then time of journey is reduced by 4 hours i.e., when speed is (x+6)km/hr, time of journey is (y−4) hours.

∴ Distance covered =(x+6)(y−4)

⇒xy=(x+6)(y−4) [Using (i)]

⇒−4x+6y−24=0 ⇒−2x+3y−12=0 ..(ii)

When the speed is reduced by 6 km/hr, then the time of journey is increased by 6 hours i.e., when speed is (x−6) km/hr, time of journey is (y−6) hours.

∴ Distance covered =(x−6)(y+6)

⇒xy=(x−6)(y+6) [Using (i)]

⇒6x−6y−36=0 ⇒x−y−6=0 (iii)

Thus, we obtain the following system of equations:

−2x+3y−12=0 x−y−6=0

By using cross-multiplication, we have,

3×−6−(−1)×−12 x = −2×−6−1×−12 −y = −2×−1−1×3 1 ⇒ −30 x = 24 −y = −1 1 ⇒x=30 and y=24

Putting the values of x and y in equation (i), we obtain

Distance =(30×24)km =720km.

Hence, the length of the journey is 720km.

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## A train covered a certain distance at a uniform speed. If the train would have been 6 km/hr faster, it would have taken 4 hours less than the scheduled time. And, if train were slower by 6km/hr, it would have taken 6 hours more than the scheduled time. Find the length of the journey.

A train covered a certain distance at a uniform speed. If the train would have been 6 km/hr faster, it would have taken 4 hours less than the scheduled time.

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A train covered a certain dist...

A train covered a certain distance at a uniform speed. If the train would have been 6 km/hr faster, it would have taken 4 hours less than the scheduled time. And, if train were slower by 6km/hr, it would have taken 6 hours more than the scheduled time. Find the length of the journey.

Updated On: 27-06-2022

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## A train covered a certain distance at a uniform speed. If train would

Question 28 (Choice 1) A train covered a certain distance at a uniform speed. If the train would have been 6 km/h faster, it would have taken 4 hours less than the scheduled time. And, if the train were slower by 6 km/hr ; it would have taken 6 hours more than the scheduled time. Find the length of

**Check sibling questions**

## Question 28 (Choice 1) - CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at Oct. 5, 2022 by Teachoo

## A train covered a certain distance at a uniform speed. If the train would have been 6 km/h faster, it would have taken 4 hours lessthan the scheduled time. And, if the train were slower by 6 km/hr ; it would have taken 6 hours more than the scheduled time. Find the length of the journey.

This question is Similar to Ex.3.7 (Optional) - Chapter 3 Class 10

### Transcript

Question 28 (Choice 1) A train covered a certain distance at a uniform speed. If the train would have been 6 km/h faster, it would have taken 4 hours less than the scheduled time. And, if the train were slower by 6 km/hr ; it would have taken 6 hours more than the scheduled time. Find the length of the journey. Let Speed of train = x km/h & Time taken = y hours. We know that, Speed = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒/𝑇𝑖𝑚𝑒 Distance = Speed × Time Distance = xy If the train would have been 6 km/h faster I.e. Speed = x + 6 It would have taken 4 hours less i.e. Time = y − 4 Now, Distance = Speed × time Distance = (x + 6) (y − 4) Putting Distance = xy from Equation (1) xy = (x + 6) (y − 4) xy = x (y − 4) + 6 (y − 4) xy = xy − 4x + 6y − 24 4x − 6y + 24 = xy − xy 4x − 6y + 24 = 0 2(2x − 3y + 12) = 0 2x − 3y + 12 = 0 Also, If the train were slower by 6km/h Speed = x − 6, it would have taken 6 hours more Time = y + 6. Now Distance = Speed × time Distance = (x − 6) (y + 6) Putting Distance = xy from equation (1) xy = (x − 6) (y + 6) xy = x (y + 6) − 6(y + 6) xy = xy + 6x − 6y − 36 xy − xy = 6x − 6y − 36 6x − 6y − 36 = 0 6(x − y − 6) = 0 x − y − 6 = 0 Hence, the equations are 2x − 3y + 12 = 0 …(2) x − y − 6 = 0 …(3) From equation (3) x − y − 6 = 0 x = y + 6 Putting (4) in equation (2) 2x − 3y + 12 = 0 2(y + 6) − 3y + 12 = 0 2y + 12 − 3y + 12 = 0 2y − 3y + 12 + 12 = 0 −y + 24 = 0 24 = y y = 24 Putting y = 12 in equation (4) x = y + 6 x = 24 + 6 x = 30 Thus, Speed of train = x = 30 km/ h & Time taken by the train = y = 24 hours Now, Distance = Speed × time Distance = 30 × 24 Distance = 720 km

**Next**: Question 28 (Choice 2) →

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### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Guys, does anyone know the answer?