Question

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

Answer 1

See the Attachment..........

Answer 2

Given :

• Total distance between Delhi and Agra = 200 km .
• speed at first 100 km = 50 km/hr

To find :

• Time so that average speed = 70km/hr

Solution :

By the formula of time ,

$\tt \: time = \dfrac{distance}{speed}$

$\tt T_1 = \dfrac{100}{50}$

$\tt T_1 = 2\ hrs$

Formula of Average speed is given by :

$\boxed{\tt Average\ speed = \dfrac{Total\ distance}{Total\ time}}$

$\tt average \: speed \: = \frac{total \: distance}{t_1 + t_{2}}$

$\tt \implies 70 = \frac{200}{2 + t_{2} }$

$\implies \tt 70(2 + t_{2}) = 200$

$\implies \tt 140 + 70 t_{2} = 200$

$\implies \tt 70 t_{2} = 200 - 140$

$\implies \tt 70 t_{2} = 60$

$\implies \tt t_{2} = \dfrac{60}{70} = \dfrac{6}{7}\ hours$

Speed in next 100 km :

$\tt \: speed = \dfrac{distance}{time}$

$\implies \tt \dfrac{100}{ \dfrac{6}{7} }$

$\implies \tt \dfrac{100 \times 7}{6}$

$\implies \tt \: 116.67 \: kmhr {}^{ - 1} (approx)$

$\sf{ \underline{so \: the \: speed \: required \: for \: second \: }} \\ \sf\underline{part \: of \: journey \: is \: 116.67 \: km {hr}^{ - 1} }$