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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 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.

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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 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. 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. 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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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/h faster, it would have taken 4 hours less than the scheduled time. And, if the train was slower by 6 km/h it

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 was slower by 6 km/h it 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 was slower by 6 km/h it would have taken 6 hours more than the scheduled time. Find the length of the journey

### SOLUTION

Let the speed of the train be x km/hr.

Let the time taken to travel certain distance be y hrs.

We know that, speed × time = distance

∴ Distance = xy km

According to the first condition, if the train would have been 6 km/h faster, it would have taken 4 hours less than the scheduled time.

∴ (x + 6)(y – 4) = xy

∴ xy – 4x + 6y – 24 = xy

∴ – 4x + 6y – 24 = 0

∴ 2x – 3y = –12     ......(i)

According to the second condition, if the train was slower by 6 km/hr, it would have taken 6 hours more than the scheduled time.

∴ (x – 6)(y + 6) = xy

∴ xy + 6x – 6y – 36 = xy

∴ 6x – 6y – 36 = 0

∴ x – y = 6   ......(ii)

Multiplying both sides by 2, we get

2x – 2y = 12   ......(iii)

Subtracting equation (iii) from (i), we get

2x – 3y = –12 2x – 2y = 12 –      +       – – y = – 24 ∴ y = 24

Substituting y = 24 in equation (ii), we get

x – 24 = 6 ∴ x = 30

∴ Length of the journey = xy

= 30 × 24 = 720 km

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method

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Chapter 1: Linear Equations in Two Variables - Q.4

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SCERT Maharashtra Question Bank 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board 2021

Chapter 1 Linear Equations in Two Variables

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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. Home > English > Class 10 > Maths > Chapter >

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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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