Question

A train covers a diatance of 300km at certain average speed . if its spedd were decreased by 10km/hr , the journey would take take 1 hour longer . What is the average speed of the train ?​

Answer 1

Let the Average speedof the train = V km/hr

Distance covered = S = 300 km

Time taken = T = S/V = 300/V --------- (1)

Decreased speed = V - 10 km/hr

Time taken = S/(V - 10) = 300/(V - 10) = T + 1 -------- (2)

Subtracting (1) from (2) we have :

300{1/(V - 10) - 1/V} = 1

{(1/(V - 10) - 1/V} = 1/300

=> {V - (V - 10)}/{V(V - 10)} = 1/300

=> 10/{V(V - 10)} = 1/300

=> V(V - 10)/10 = 300

=> V² - 10V = 3000

=> V² - 10V - 3000 = 0

=> V² + 50V - 60V - 3000 = 0

=> V(V + 50) - 60(V + 50) = 0

=> (V + 50)(V - 60) = 0

=> (i) V + 50 = 0 , or (ii) V - 60 = 0

=> (i) V = - 50 , or (ii) V = 60

Rejecting the negative value, we get V = 60

Hence the average speed of the train = 60 km/hr

Hope this will help you ☺