Question

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

Answer 1

Total distance travelled = 200 Km

First 100 Kilometers :-

Speed of train = 50 Km/hr

Distance = 100 km

Time = Distance /speed

Time = 100/50 = 2hr

Next 100 Kilometers :-

Distance = 100 km

Speed = x km/hr

Time = Distance /speed

Time = 100/x hr

Now,

Total time taken =

$2 + \frac{100}{x} \\ \\ \\ \\ = \frac{2x + 100}{x}$

Now,

Average speed = Total distance /total time.

So,

We have :-

Average Speed =

$\frac{200}{ \frac{2x + 100}{x} } = 70 \\ \\ \\ \\ \frac{200x}{2x + 100} = 70 \\ \\ \\200x = 140x + 7000 \\ \\ \\200x - 140x = 7000 \\ \\ \\60x = 7000 \\ \\ \\x = \frac{7000}{60} \\ \\ \\x = 116.66 \: kmph$