Question

If a train runs at 40 kilometre per hour It reaches its destination late by 11 minutes but if it's run at 50 km per hour it is late by 5 minutes only find the distance to be covered by the train .​

Answer 1

Answer:

Let the correct time for the train to complete the journey is x minuets

Then train cover distance in x+11 minuets at speed 40 km\hr =

60

40(x+11)

km

Then train cover distance in x+5 minuets at speed 50 km\hr =

60

50(x+5)

km

Both are same then

60

40(x+11)

=

60

50(x+5)

∴40x+440=50x+250

∴−10x=−190

∴x=19 minutes

hope it is correct

we can't find exact distance bcz in your question the speed for exact time is not given

Answer 2

Answer:

Let the usual time(time without getting late)= x

And usual speed (speed without getting late)=y

Actual distance covered = xy

If it run by 40 km/h it is late by 11min

So we have

40×((x+11)/60)=xy

(40x+440)/60 = xy ……..(1)

If it run by 50km/h it is late by 5 minutes

So we have

50×((x+5)/60) = xy

(50x+250)/60=xy……….(2)

subtract (2) from(1)

-10x +190/60 =0

x=190/600

So it will take 19 minutes to complete the journey.

Put value in equation (2)

(950+250)/60 =xy

xy =20

so it will cover 20 km in each case.

………………………Second way…………………..

…………………………………………………………………………..

Let distance covered = x

And time =y

time = distance /speed

So we have

x/40 = y+11/60

x=40y+22/3

x-40y=22/3

multiply by 5

5x-200y =110/3………………..…(1)

Now again time = distance / speed

So we have

x/50= y+5/60

x-50y=25/6

multiply by 4

4x-200y =100/6

4x-200y=50/3…………………….(2)

sub ( 2 ) from (1)

x= (110-50)/3

x=20

so distance is 20 km