Question

train R takes 5 hours less than train S for covering a distance of 750km. if the average speed of train R is 25km/hr more than that of train S find the average speed of both the trains.​

Answer 1

Answer:

60 km/h

Step-by-step explanation:

Let x hour be the time taken by by train R

Time taken by train S = (x + 5) hours

Distance = 750 km

Find the speed of R in term of x:

speed = distance ÷ time

speed = 750/x

Find the speed of S in term of x:

speed = distance ÷ time

speed = 750/(x + 5)

Given the difference in speed is 25km/h:

750/x - 750/(x + 5) = 25

750(x + 5) - 750(x - 5) = 25x(x + 5)

30(x + 5) - 30(x - 5) = x(x + 5)

30x + 150 - 30x + 150 = x² - 5x

x² - 5x - 300 = 0

(x + 20) (x - 15)  = 0

x = 15 or - 20 (rejected)

Find the total time taken:

Time taken by R = x = 15 hour

Time taken by S = x - 5 = 15 - 5 = 10 hours

Total time taken = 15 + 10 = 25 hours

Find the total distance:

Total distance traveled = 750 x 2 = 1500 km

Find the average speed:

Average Speed = 1500 ÷ 25 = 60 km/h

Answer: 60 km/h