Question

a train runs at 40 km per hour it reaches its destination late by 11 minutes but if it runs at 50 km per hour it is late by 5 minutes only find the distance covered by the train​

Answer 1

Step-by-step explanation:

Average speed is defined as the total distance covered by a body divided by the time taken by the body to cover it.

∴average velocity=distance covered/time taken

Now, starting with the solution to the above question. Let the actual time taken be t hours and the distance to be travelled be x km.

When the train was moving with a speed of 40 km/hour, it takes 11 min i.e. 1160 hours more than the actual time. We can represent this in the form of mathematical equation as:

average velocity =distance covered/time taken

⇒40=x/t+11/60. (i)

Also, it is mentioned that when the train was moving with a speed of 50 km/hour, it takes 5 min, i.e., 560 hours more than the actual time. We can represent this in the form of mathematical equation as:

average velocity=distance coveredtime taken

⇒50=x/t+5/60.(ii)

Now we will divide equation (ii) by equation (i). On doing so, we get

50/40=x/t+5/60 / x/t+11/60

⇒5/4=t+11/60t+5/60

Now to further solve the equation, we will cross-multiply. On cross-multiplication, we get

5(t+560)=4(t+1160)

⇒5t+2560=4t+4460

⇒t=1960 hours = 19 minutes

Therefore, the actual time train should take is 19 minutes.