A train travels at a speed of 60 km/h for 0.52 h, at 30 km/h for the next 0.24 h and then at 70 km/h for the next 0.71 h. What is the average speed of the train ?

A train travels at a speed of 60 km/h for 0.52 h, at 30 km/h for the n

1.	A train travels at a speed of 60 km/h for 0.52 h, at 30 km/h for the next 0.24 h and then at 70 km/h for the next 0.71 h. What is the average speed of the train ?
Answer» In this problem, first of all we have to calculate the distances travelled by the train under three different conditions of speed and time. (i) In the first case, the train travels at a speed of 60 km/h for a time of 0.52 hours. Now, `" "` Speed = `("Distance")/("Time")` So, `" "60 = ("Distance")/(0.52)` And, `" "` Distance = 60 `xx` 0.52 `" "`=31.2 km `" "`...(1) (ii) In the second case, the train travels at a speed of 30 km/h for a time of 0.24 hours. Now, `" "` Speed= `("Distance")/("Time")` So, `" "30=("Distance")/(0.24)` And, `" "` Distance = 30 `xx` 0.24 `" "=7.2` km `" "`...(2) (iii) In the third case, the train travels at a speed of 70 km/h for a time of 0.71 hours. Again, `" "` Speed = `("Distance ")/("Time")` so, `" " 70 = ("Distance")/( 0.71)` And, `" "` Distance = 70 `xx` 0.71 `" "` = 49.7 km `" "`...(3) Now, from the equation (1), (2) and (3), we get : Total distance travelled = 31.2+7.2+49.7 `" "` = 88.1 km `" "` ...(4) And, Total time taken = 0.52+0.24+0.71 `" "` = 1.47 h `" "...(5) We know that : `" "` Average speed = `("Total distance travelled")/("Total time taken")` `" "` = ` (88.1)/(1.47)` `" "` = 59.9 km/h