Question

A train covers a distance of 90 km at a uniform speed if the speed had been 15 km per hour more it would have taken half an hour less for the journey find the original speed of the train

Answer 1

Answer:

Given, distance = 90 km

let speed (original) = x km/h

time taken to travel = 90/x hr

∴ New speed  = (x+15) km/hr

Time taken to travel = 90/(x+15) hr

∴ 90/x = 90/(x+15) + 1/2

⇒ 90/x - 90/(x+15) = 1/2

⇒ 90(1/x - 1/(x+15)) = 1/2

⇒ x+15-x/x(x+15) = 1/2 ×1/90 

⇒ 15/x(x+15) = 180

⇒ x(x+15) = 15 × 180 = 2700

⇒ x² + 15x - 2700 = 0

→x² + 60x - 45x+2700 = 0 [Quadratic Equation]

⇒(x+60)(x-45) = 0

⇒x = 45 or - 60

∵ Speed can't be negative..

∴ Original speed = 45km/hr