Question

The distance between Delhi and Agra is 200km a train travels the first 100km at speed of 50km/h how fast must the train travel next 100km so that the average speed is 70km/h for the whole journey

Answer 1

Step 1:Given:

$d_1=100\text{km}$

$d_2=100\text{km}$

$v_1=50\frac{\text{km}}{\text{h}}$

$v_{avg}=70\frac{\text{km}}{\text{h}}$

Step 2: Calculate speed in next $100\text{km}$.

$$\begin{gathered} v_{avg}=\frac{\text{Total distance}}{\text{Time}} \\ =\frac{d_1+d_2}{{\displaystyle \frac{d_1}{v_1}}+{\displaystyle \frac{d_2}{v}}} \\ 70\frac{\text{km}}{\text{h}}=\frac{100\text{km}+100\text{km}}{{\displaystyle \frac{100}{50}}+{\displaystyle \frac{100}{v}}} \\ v=\frac{700}{6}\frac{\text{km}}{\text{h}} \end{gathered}$$

Hence, the train needs to travel at a speed of $116.66km/h$so that the average speed is $70km/h$ for the whole journey