A train travels first 30 miles at a speed of 15 miles/hour and the next 30 miles at a speed of 30 miles/hour . Find the average velocity of the train.

Explanation

Here, the total distance =(30+30) miles =60 miles
Total times required `=((30)/(15)+(30)/(30))` hours =(2+1) hours =3 hours .
`therefore ` the average velocity of the train `=(60)/(3)` miles/hour=20 miles/hour.
By using the formula of harmonic meanm, we can also find the required average
The train has travelled same distance with two types of velocities . These two velocities are 15 miles/hour and 30 miles/hour. The harmonic mean of these two types of velocities.
`(2)/((1)/(15)+(1)/(30))=(2)/((2+1)/(30))=2xx(30)/(3)=20`
`therefore ` the required averge =20 miles/hour.