A train covered a certain distance at a uniform speed. If a train would have been 6 km/h, it would have taken 4 hours less than the schedule time.
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Answer:
10th
Maths
Pair of Linear Equations in Two Variables
Algebraic Solution of a Pair of Linear Equations
A train covered a certain d...
MATHS
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Asked on November 22, 2019 by
Peru Pintu
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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ANSWER
Let the actual speed of the train be x km/hr and the actual time taken be y hours. Then,
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.
Explanation:
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10th
Maths
Pair of Linear Equations in Two Variables
Algebraic Solution of a Pair of Linear Equations
A train covered a certain d...
MATHS
avatar
Asked on November 22, 2019 by
Peru Pintu
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.
MEDIUM
Help best friend
Study later
ANSWER
Let the actual speed of the train be x km/hr and the actual time taken be y hours. Then,
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
X /3×-6(-1) ×-12 -2× -6-1×12
=1/-2 -1 -1×3
=ꉧ/-30 - -ꌦ/24 -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.