Question

The distance between Delhi and Agra is 200 km. A train travels the first 100 km at a speed of 50 km/h. How fast must the train travel the next 100 km, so as to average 70 km/h for the whole journey ?

Answer 1

Step 1, Given data

The total distance = 200 km

Let total time be 't ' hours

The speed of the train for the first 100 km is 50 km/hr

Average speed = 70 km/h

Step 2, Finding speed for the next part

Time taken for the first 100 km

$t_1$ = $\frac{Distance}{Speed}=\frac{100}{50}=2h$

We know,
Average speed = $\frac{Totaldistance}{Totaltime}$

$S_2$ = next 100 km traveled by train.
$t_2$ =time taken to travel next 100 km

Now,

70 km/h = $\frac{S_1+S_2}{t_1+t^{}}$ =$\frac{200}{2+t_2}$
After solving
140+70 $t_2$ =200
70 $t_2$ =60

$t_2$ =$\frac{6}{7}$ hours.

The speed required by train to travel the next 100 km so as to attain a 70 km/h average speed is:
speed($v_2$ ) = $\frac{Distance}{Time}$
We have the remaining distance to cover = 200 -100 = 100 Km
We have the remaining time is = $\frac{6}{7}$ Hours

Find the final speed = $\frac{100Km}{\frac{6}{7}hr}$ = $\frac{100Km\times 7}{6hr}$ = 116.67 $\frac{Km}{hr}$

Hence the speed for the next part is 116.67 km/h