A train travels the first 15 km at a uniform speed of 30 km/h; the next 75 km at a uniform speed of 50 km/h; and the last 10 km at a uniform speed of 20 km/h. Calculate the average speed for the entire train journey.
(i) In the first part, train travels at a speed of 30 km/h for a distance of 15 km.
Speed = \(\frac{Distance}{Time}\)
Time = \(\frac{Distance}{Speed}\)
t1 = \(\frac{15}{30}\) = \(\frac{1}{2}\)h
(ii) In the second part, train travels at a speed of 50 km/h for a distance of 75 km.
t2 = \(\frac{75}{50}\) = \(\frac{3}{2}\)h
(iii) In the third part, train travels at a speed of 20 km/h for a distance of 10 km.
t3 = \(\frac{10}{20}\) = \(\frac{1}{2}\)h
Total distance covered = 15 + 75 + 10 = 100 km
Total time taken = \(\frac{1}{2}\) + \(\frac{3}{2}\) + \(\frac{1}{2}\) = \(\frac{5}{2}\)h
Average speed = \(\frac{Total\;distance\;covered}{Total\;time\;taken}\)
= \(\frac{100}{\frac{5}{2}}\) = 40 km/h