Question

A train moving with uniform speed for a certain distance takes 6 hours less if its speed be
increased by 6 km/hour. It would have taken 6 hours more, had its speed been decreased by 4 km/hr. Find the distance travelled of the journey and the speed of the train.

Answer 1

Answer:

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

Step-by-step explanation:

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

Step-by-step explanation:

distance= speed ×time

let the distance =y km/hr

let the speed = X km/ hr

case 1

increased speed =X+6 km/hr

time reduced = y-6

distance (xy)= speed× time

xy = (X+6) (y-6)

xy= xy - 6x+6y-36

6x-6y+36=0

6(x-y+6) =0

x-y+6 =0 _______(1)

case 2

increased time= y+6

decreased speed= x-4

distance (xy) = (y+6) (x-4)

xy= xy- 4y +6x -24

4y-6x+24 =0

2(2y-3x+12)=0

-3x+2y +12= 0

3x -2y -12 =0______(2)

x-y+6 =0____(1)×3

3x-2y-12=0_____(2)

subtracting

3x-3y+18=0

3x-2y-12=0

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

-y+30 =0

-y= -30

y=30

substituting y=30 in (1)

x-y+6= 0

x-30+6= 0

x-24= 0

X=24

speed of train = 24 km/hr

distance= xy = 24×30

=720 km