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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/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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    Mohammed 8 day ago
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