#### 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.

#### Solution

(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,

t_{1} = `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 ,

t_{3} = `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