Question

A man runs a distance of 50m in 8s. If he continues to run at the same speed for another 3 minutes, what will be the total distance he covers? Also, find his speed in km/hr.

Answer 1

Hint: In order to solve this question, we need to know the formula of speed that is speed is calculated by finding the ratio of the distance travelled by an object to the time taken by the object to travel that distance. Mathematically, we can write it as,
$$\text{Speed}={\displaystyle \frac{\text{Distance travelled}}{\text{Time taken}}}$$

Complete step-by-step answer:
In this question, we are asked to find the distance covered by a man in 3 minutes and also the speed in km/hr. We are given that a man covers a 50m in 8s. So, let us consider the speed of the man is x m/sec. And we know that speed of an object is nothing but the ratio of the distance travelled by an object to the time taken by the object to travel that distance. Mathematically, we can write it as,
$$\text{Speed}={\displaystyle \frac{\text{Distance travelled}}{\text{Time taken}}}$$
To this equation, we will substitute the values of distance, time and speed, we will get,
$$x={\displaystyle \frac{50}{8}}....\left(i\right)$$
Now, we have been given that the man runs with a constant speed. So, the speed of the man will again be x m/sec. Now, we have to find the distance travelled by the man in 3 minutes which is same as $$3\times 60\sec$$, because 1 minute = 60 seconds. Therefore, we can write,
$$x={\displaystyle \frac{\text{Distance}}{3\times 60}}$$
Now, we will cross multiply the equation. So, we will get,
$$x\times 3\times 60=\text{Distance}$$
Now, from equation (i), we will put the values of x. So, we will get,
$$\text{Distance = }{\displaystyle \frac{50}{8}}\times 3\times 60$$
Distance = 1125m.
Hence, the distance travelled by a man in 3 minutes is 1125m. Now, we are asked to find the speed of the man in km/hr. So, we can write,
$$x={\displaystyle \frac{50}{8}}$$
As we have taken speed in m/sec and we have to calculate in km/hr. So, we will divide the speed by 3600 and multiply it by 1000. By using the conversion rule, 1 km = 1000m and 1 hour = 3600 sec. Therefore, we can write,
$${\displaystyle \frac{x\times 1000}{3600}}={\displaystyle \frac{50}{8}}$$
$$x={\displaystyle \frac{50}{8}}\times {\displaystyle \frac{3600}{1000}}$$
$$x={\displaystyle \frac{5\times 36}{8}}$$
$$x=22.5km/hr$$
Hence, the speed of the man is 22.5 km/hr. And he covered a distance of 1125m in 3 minutes.

Note: In this question, the possible mistake one can make is by not covering the minutes into seconds or maybe by ignoring the word ‘km/hr’ in question. We should know the conversion rule of minutes to seconds, that is 1 minute = 60 seconds and hours to second, that is 1 hour = 60 minutes = 60 $$\times$$ 60 seconds, and also 1 km = 1000 m.