Question

A train 100 m long is approaching an unmanned railway crossing. The train is
travelling at a uniform speed of 90 km/hr and is 1 km away from the crossing. At the
same time, a bus, also approaching the crossing, is 700 m away from it. Assuming the
bus is also travelling at a uniform speed of B, at what range of B (rounded to whole
number) will the bus collide with the train?
A. 59 km/hr <B< 61 km/hr
B. 57 km/hr <B<63 km/hr
C. 55 km/hr< B < 65 km/hr
D. None of these​

Answer 1

Answer:

im pretty sure it's C if not please correct me

Step-by-step explanation:

Answer 2

The correct option is B. 57 km/hr <B<63 km/hr.

Given:

A train 100 m long is approaching an unmanned railway crossing. The train is travelling at a uniform speed of 90 km/hr and is 1 km away from the crossing. At the same time, a bus, also approaching the crossing, is 700 m away from it.

To find:

Assuming the bus is also travelling at a uniform speed of B, at what range of B (rounded to whole number) will the bus collide with the train?

Solution:

There is one range of speed with which bus can travel.

Either the bus can collide at the starting point of train or the rest of the train.

So, we will find out the speed of bus if it hits the train's starting point and if it hits the train's last point. By this we will get a range of speed.

Let's suppose, the end of tunnel is the point where the bus collides

So speed of train = 90 km/hr

Distance from front part to end of tunnel = 1 km

Time taken = distance / speed = 1/90 hr

Now, both train and bus have to take same time to reach that point to collide.

Distance travelled by bus =  700m = 0.7 km

Time taken by bus = time taken by train = 1/90 h

Speed of bus = distance / time = 0.7/ (1/90) = 0.7 * 90 = 63 km/hr

Now, we will calculate speed by taking end point of train

Distance covered by end point of train = length of tunnel + length of train = 1 km + 100 m = 1.1 km

Speed of train = 90 km/h

Time taken by train = distance / speed = 1.1/90 h

Now, the bus has to cover 700 m in 1.1/90 h

Speed of bus = distance / train = 0.7 / (1.1/90)

= (0.7 * 90)/1.1 = 63/1.1 = 57.27 km/h = 57 km/h

Hence, the speed of bus should be between 57km/h and 63 km/h.

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