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A man covers first half of the distance with a speed of 30 km /hr and the remaining distance with a speed of 70 km /hr .Find the Average speed of the Man

Let total distance be x according to question x / 2 distance cover in time t1 ,so x / 2 = 30*t1 ...............(1) x / 2 distance cover in time t2 ,so x / 2 = 70*t2.................(2) average speed = total distance / total time = x / t ( where t = t1 + t2) multiply by 7 / 3 in equation (1) 7x / 6 = 70*t1..................(3) add equation (2) and (3) we get , 10x / 6 = (t1 + t2)*70 x / (t1 + t2) = 42 hence average speed = 42 Km / hr

we can use the shortcut formula , when body travels equal distances with different velocities the average velocity is given by 2*(product of velocities) / sum of velocities