Question

The distance between delhi and agra 200km, a train travells the first 100 km at speed of 50km/h how fast must the train travel the next 100 km so as to average speed 70om/hfor the whole journey

Answer 1

Answer:

Distance between delhi and agra = 200m

Let train travells first half of the total distance at speed of 50kmph and second half of the total distance at speed of Vkmph.

Average speed of train = 70kmph

Calculation :

When a body covers first half distance at speed V_1 and second half distance at speed V_2, then average speed during the entire journey is given by

$\bigstar\underline{\boxed{\bf{\red{V_{av}=\dfrac{2V_1V_2}{V_1+V_2}}}}}$

$\dashrightarrow\sf\:70=\dfrac{2(50)(V)}{50+V}\\ \\ \dashrightarrow\sf\:3500+70V=100V\\ \\ \dashrightarrow\sf\:30V=3500\\ \\ \dashrightarrow\underline{\boxed{\bf{\blue{V=116.67\:kmph}}}}\:\orange{\bigstar}$

✴ Extra Dose :

❇ If a particle moves in two equal intervals of time at different speed V_1 and V_2 respectively, then

$\bigstar\:\underline{\boxed{\bf{\gray{V_{av}=\dfrac{V_1+V_2}{2}}}}}$

❇ When particle covers one-third distance at speed V_1, next one-third at speed V_2 and last one-third at speed V_3, then

$\bigstar\:\underline{\boxed{\bf{\green{V_{av}=\dfrac{3V_1V_2V_3}{V_1V_2+V_2V_3+V_3V_1}}}}}$

Answer 2

Answer :

We have the following data to find the speed for the second part of the journey:

Total distance to be travelled by train (D) = 200 km

Average speed required (vavg) = 70 km/hr

Time required for the entire journey (T) :

Time = Total Distance/Average speed

= `200/70` hr

T = 20/7 hr

For the first part of the trip:

Distance covered (d1) = 100 km

Speed for this part of journey (v1) = 50 km/hr

Time taken for the first part of journey :

Time = Distance travelled/Speed

So,

t1 = 100/50 hr

= 2 hr

For the second part of the trip,

Distance covered (d2) = 100 km

Time taken for the second part of journey :

t2 = T-t1

= (20/7 - 2) hr

= 6/7 hr

Speed of the train for the second part of the journey :

= distance travelled/Time

= ((100)(7))/6

= 116.67 km/hr

$\rule{200}{2}$