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A train is moving at a uniform speed of 75 km/hour. (i) How far will it travel in 20 minutes? (ii) Find the time required to cover a distance of 250 km. - Mathematics

Sum
A train is moving at a uniform speed of 75 km/hour.
(i) How far will it travel in 20 minutes?
(ii) Find the time required to cover a distance of 250 km.
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Solution

Let the distance travelled (in km) in 20 minutes be x and time taken (in minutes) to cover 250 km be y.
Distance travelled (in km) 75 x 250
Time taken (in minutes) 60 20 y
Since the speed is uniform, therefore, the distance covered would be directly
proportional to time.
(i) We have `75/60 = x/20`
or `75/60 xx 20 = x`
or x = 25.
So, the train will cover a distance of 25 km in 20 minutes.
(ii) Also, `75/60 = 250/y`
or `y = (250 xx 60)/75` = 200 minutes or 3 hours 20 minutes.
Therefore, 3 hours 20 minutes will be required to cover a distance of 250 kilometres.
Alternatively, when x is known, then one can determine y from the relation `x/20 = 250/y`.
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