Time and Distance
Math MCQs

Question :    An athlete takes 30 second to complete a race of 450 meter. Find the speed of the athlete in kilometre per hour.

Correct Answer  54 kilometer/hour

Solution & Explanation

[Strategy to solve the Question: (1) Calculate the speed in m/s and then change this speed into kilometre per hour. (2) change the distance into km and time into hour and then calculate the speed using these units. This speed will be in the required kilometer per hour]

Given,

Distance = 450 meter

Time = 30 second

Now we know that,

Speed = ^Distance/_Time

Thus, speed of the given athlete

= ^{450 meter} /_{30 second}

= 15 meter per second

⇒ Speed = 15 m/s

Conversion of speed from m/s to km/h

To convert meter per second (m/s) to kilometre per hour (km/h) we need to multiply m/s by ¹⁸ /₅ .

Thus, 15 m/s

= 15 3 × ¹⁸ / ₅ km/h

= 3 × 18 = 54 km/h

Thus, speed of the given athlete = 54 km/h Answer

Second method to calculate the speed in km/h using distance given in meter and time given in second.

Here, given distance = 450 meter

= ⁴⁵⁰ /₁₀₀₀ km

[∵ 1000 meter = 1 km. Thus, 1 meter = ¹ /₁₀₀₀ km]

= ⁴⁵ /₁₀₀ km

Thus, distance = 0.45 km

And, given time = 30 second

= ³⁰ /_{60 × 60} hour

= ³⁰/_{3600 120} hour

= ¹/₁₂₀ hour

Thus, time = ¹/₁₂₀ hour

Calculation of speed in km/h using formula

Now we know that,

Speed = ^Distance/_Time

Thus, the speed of the given athlete in km/h

= ^{0.45 km} /_{¹/120 hour}

= 0.45 km × ¹²⁰/_{1 hour}

= 0.45 × 120 km/h

= 54 kilometer per hour

Thus, speed of the given athlete = 54 km/h Answer

[After observing the result obtained here, it is better to calculate the speed in m/s using the given units and after that change the speed from m/s to the required km/h.

The using of type of method depends upon the situation. ]

Calculation of speed using Unitary Method when time and distance are given]

Given, Distance = 450 meter

And, Time = 30 second

∵ In 30 second, the distance covered = 450 m

∴ In 1 second, the distance covered = ^{450 m} /_{30 second}

= 15 m/s or 15 meter per second

Conversion from m/s to km/h

Here, speed = 15 m/s

This means, speed = ^{15 m}/_{1 s}

= ^{15/₁₀₀₀ km}/_{¹/60 × 60 hour}

= ^{15/₁₀₀₀ km}/_{¹/3600 hour}

= ¹⁵/₁₀₀₀ km × ³⁶⁰⁰/_{1 hour}

= ^{15 × 36}/₁₀ km/h

= ⁵⁴⁰/₁₀ km/h

⇒ Speed in km/h = 54 km/h

Thus, speed of the given athlete = 54 km/h Answer

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(3) By running at a speed of 23 km/h how much distance a car will cover in 5 second?

(4) At a certain speed a cyclist covers a distance of 74 km in 3 hours. How much distance will it cover in 4 hour?

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(6) At a certain speed a cyclist covers a distance of 96 km in 3 hours. How much distance will it cover in 4 hour?

(7) Find the distance covered by a moving object in 28 hours if it covers a distance of 66 km in 18 hours.

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