Question

A train is moving at a uniform speed of \[75{\rm{km/hour}}\].
(i)How far will it take in 20 minutes?
(ii)Find the time required to cover a distance of 250 km.

Answer 1

Hint: Here the uniform speed of the train is given. We will first find the distance covered by the train in 1 hour and then in 1 minute using the unitary method. Then we will find the distance covered by the train in 20 minutes. Similarly, we will find the time taken to cover 1 km using the unitary method and then we will find the time taken to cover 250 km distance.

Complete step-by-step answer:
It is given that the uniform speed of the train is \[75{\rm{km/hour}}\].
We will use the unitary method now.
Distance covered by the train in 1 hour \[ = 75km\]
We can write the same statement as
Distance covered by the train in 60 minutes \[ = 75km\]
Distance covered by the train in 1 minute \[ = \dfrac{{75km}}{{60}}\]
We have to find the distance covered in 20 minute.
Using unitary method, we get
Distance covered by the train in 20 minute \[ = \dfrac{{75km}}{{60}} \times 20 = 25km\].
Hence, the train will cover \[15km\] in 20 minutes.
As the uniform speed of the train is \[75km/hour\].
We can it as:-
Time required to cover a distance of\[75km\] \[ = 1hour\]
Therefore, time required to cover a distance of \[1km\] \[ = \dfrac{1}{{75}}hour\]
Using unitary method, we get
Thus, time required by the train to cover a distance of \[250km\] \[ = \dfrac{1}{{75}} \times 250hour = 3.3hours\]

Note: We need to know the basic formulas to solve the distance questions. Distance covered by any object or vehicle is equal to the product of the time taken to cover that distance and speed of that vehicle or object. We can write the above relation between distance covered, time taken and speed of that object mathematically as:- \[dis\tan ce = speed \times time\]