Question

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.

Answer 1

(i) In the first case, the train travels at a speed of 30 km/h for a distance of 15 km.
We can find the time as :
`"Time" = "Distance travelled"/"Speed"`
S0,
t₁ = `15/30` hr
= 0.5 hr
(ii) In the second case, the train travels at a speed of 50 km/h for a distance of 75 km.
We can find the time as :
`"Time" = "Distance travelled"/"Speed"`
So , 

t_{2 =} `75/50` hr
= 1.5 hr
(iii) In the third case, the train travels at a speed of 20 km/h for a distance of 10 km.
We can find the time as :
`"Time" = "Distance travelled"/"Speed"`
So , 
t₃ = `10/20` hr

 = 0.5 hr
Total distance covered :
= (15 + 75 + 10) km
= 100 km
Total time taken = (0.5 + 1.5 + 0.5) km
= 2.5
Therefore , Average speed = `"Total distance travelled"/"Time"`
Now , put the values to get the average speed . 
= `100/2.5` 
= 40 km/hr