The distance between Delhi and Agra is 200 Km. A train travels the first 100 Km at a speed of 5 K/h . How fast must the train travel the next 100 Km , so as to average 70 K/h for the whole journey ?
To average at a speed of 70 km/h for the entire 200 km would take
200/70 hrs or appr 2.86 hrs
but going only 5 km/h for the first 100 km already took
100/5 hrs or 20 hrs. so it not possible to average 70 km/h for the whole trip
This is a common "trick" question that has been around in various forms
for a long time.
Usually the first leg is given with more reasonable data
e.g. doing the first 100 km at 25 km/h would have been a more reasonable situation
but led to the same conclusion.
To find the speed the train must travel for the next 100 km, let's first calculate the total time taken for the journey using the given information.
We know that speed = distance / time. Rearranging the equation, we have time = distance / speed.
For the first 100 km, the train travels at a speed of 5 km/h, so the time taken is 100 km / 5 km/h = 20 hours.
Now, let's assume the speed the train needs to travel for the next 100 km is x km/h.
The time taken for the next 100 km would be 100 km / x km/h = 100/x hours.
The total distance for the entire journey is 200 km, and the total time taken is 20 hours for the first 100 km + 100/x hours for the next 100 km.
So, the average speed for the whole journey is total distance / total time = 200 km / (20 + 100/x) hours.
Given that the average speed for the whole journey should be 70 km/h, we can set up the equation:
70 km/h = 200 km / (20 + 100/x) hours.
To solve for x, let's cross-multiply and simplify the equation:
70 km/h * (20 + 100/x) hours = 200 km.
Expanding the equation:
1400 km/h + 7000/x km/h = 200 km.
Subtracting 1400 km/h from both sides:
7000/x km/h = 200 - 1400 km/h.
Simplifying:
7000/x km/h = 1600 km/h.
Cross-multiplying:
7000 km/h = 1600 km/h * x.
Dividing both sides by 1600 km/h:
(7000 km/h) / (1600 km/h) = x.
Simplifying:
x ≈ 4.375 km/h.
Therefore, the train must travel at approximately 4.375 km/h for the next 100 km to average 70 km/h for the whole journey.