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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

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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 would have taken 6 hours more than the scheduled time. Find the length of the journey

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    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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    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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