Question

A train covered a certain distance at a uniform speed. if the speed of the train had been 6 km/hr faster, it would have taken 4 hour less time than the scheduled time and if the speed of the train were slower by 6 km/hr, the train would have taken 6 hr more than the scheduled time. the length of the journey was:

Answer 1

Let x km/hr be the speed of train

Let y be the time taken by the train

Distance = speed x time

= x y

To form the first equation let us consider the given information from the question that is If the train had been 6 km/hr faster,it would have taken 4 hours less than the scheduled time.

it clearly says that speed is increased by 6 and time is reduced by 4

So , (x + 6) (y - 4) = x y

x y - 4 x + 6 y - 24 = x y

x y - x y - 4 x + 6 y = 24

- 4 x + 6 y = 24

divided by (-2) => 2 x - 3 y = -12 ----- (1)

To form the second equation let us consider the given information from the question that is If the train were slower by 6km/hr, then it would have taken 6 hours more than the scheduled time.

it clearly says that speed is reduced by 6 and time is increased by 6

So , (x - 6) (y + 6) = x y

x y + 6 x - 6 y - 36 = x y

x y - x y + 6 x - 6 y = 36

6 x - 6 y = 36

divided by (6) => x - y = 6 ----- (2)

2 x - 3 y = -12

(2) x 2 => 2 x - 2 y = 12

(-) (+) (-)

---------------

- y = -24

y = 24

Now we have to apply the value of y in the first equation to get value of x

Substitute y = 24 in the first equation we get

2 x - 3 (24) = -12

2 x - 72 = -12

2 x = -12 + 72

2 x = 60

x = 60/2

x = 30

Speed of the train = 30 km/hr

Time taken by the train = 24 hours

Distance covered by the train = x y = 30 x 24 = 720 km

Verification:

2 x – 3 y = -12

2(30) - 3(24) = -12

60 - 72 = -12

-12 = -12

Hope this helps you

Answer 2

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

Let y be the time taken by the train .

Distance =speed × time

Xy = Putting in 1 equation

So, (x+6) (y-4)=xy

xy-xy-4x+6y=24

-4x+6y=24 -- this is the 1 equation

Divided by (-2) 2x-3y= -12

there is second equation solve

So, (x-6) (y+6)=xy

xy+6x-6y-36=xy

xy-xy+6x-6y=36

6x-6y=16

Divided by 6 x-y=6--- this is the 2 equation

2x-3y=-2

(2)×2---2x-2y=12

-y=-24

y=24

Then, substitute method solve

y=24 in---1 equation

2x-72 =-12

2x=-12+72

2x=60

x=60/2

x=30

Then, we find the spped of he train = 30km

Time taken by he train =24km

Distance is coverd by train =xy

=30×24=720

2x-3y=-12

2 (30)-3 (24)=-12

60-72=-12

-12=-12

=1

Hope this solution is help u♡♡