et

r = the average speed of train R, r>0

s = the average speed of train S, s>0

the average speed of train R is 25 km/hr more than that of the train S

r = 25 + s

since avg.speed = distance/time => time = distance/avg.speed

train R takes 5 hours less than train S for covering a distance of 750 km

750/r = 750/s - 5

plug r = 25 + s into the last equation

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

by solving we find and consider the positive roots

s = 50 km/hr

click here to see the step by step solution of the equation

Click to see all the steps

r = 25 + 50

r = 75 km/hr

the average speed of train R is 75 km/hr.

the average speed of train S is 50 km/hr.