The average speed of a train running at a speed of 30 km/h during the first 100 km, at the speed of 40 km/h during the second 100 km and at the speed of 50 km/h during the last 100 km is nearly ________.

38.3 km/h

Average Speed = \(\frac{Total \;Distance}{Total \;Time}\)

Distance = Speed × Time

Time= \(\frac{Distance}{Speed}\)

T1 = \(\frac{100}{30}\) = \(\frac{10}{3}\) hours

T2 = \(\frac{100}{40}\) = \(\frac{5}{2}\) = 2 .5 hours

T3 = \(\frac{100}{50}\) = 2 hours

Total distance = 100 + 100 + 100 = 300 km

Total time = \(\frac{10}{3}\) + 2.5 + 2 = \(\frac{10 + 7.5 + 6}{3}\)

= \(\frac{23.5}{3}\)

Average speed = \(\frac{300 × 3  }{23.5}\) = 38.29 km/h

= 38.3 km/h  ( approx)

So , Average speed is 38.3 km/h