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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`.

Concept: Concept of Direct Proportion

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