Question

A runner can complete a 750 m race in two and a half minutes. Will he be able to beat another runner who runs at 17.95 km/hr?​

Answer 1

Step-by-step explanation:

Solution :

We are given that the first runner can complete a 750 m race in 2 minutes and 30 seconds or 150 seconds.

=> Speed of the first runner = 750 / 150 = 5 m / sec

We convert this speed to km / hr by multiplying it by 18/5.

=> Speed of the first runner = 18 km / hr

Also, we are given that the speed of the second runner is 17.95 km / hr.

Therefore, the first runner can beat the second runner

Things to know :-

Distance = Speed x Time

To convert from km / hour to m / sec, we multiply by 5 / 18. So, 1 km / hour = 5 / 18 m / sec

To convert from m / sec to km / hour, we multiply by 18 / 5. So, 1 m / sec = 18 / 5 km / hour = 3.6 km / hour

For a certain distance, if the ratio of speeds is x : y, then the ratio of times taken to cover the distance would be y : x and vice versa.

Answer 2

‎

Given:-

• A 750 m race can be completed by a runner- A in 2 minutes 30 seconds.
• The same distance (race) is being completed by runner- B with the speed of 17.95 kmph.

To do:-

• We've to state whether runner- A can beat runner- B in the race.

Concept:-

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎The given question is from the topic "Time and Distance". The distance covered per unit time is called speed, i.e, Speed = Distance/Time. If two bodies travel with same speed, the the distance covered varies directly as time, and it is written as Distance ∝ Time. Further, if two bodies travel for the same period of time, then the distance covered varies directly as the speed, i.e, Distance ∝ Speed. And if two bodies travel the same distance, then the time varies inversely as speed, i.e, Time ∝ 1/Speed.

Distance is usually measured in kilometres, metres, or miles; time in hours or seconds and speed in km/h or miles/h or m/s.

To convert speed in kmph to m/s, multiply it with 5/18 and to convert m/s to kmph, multiply it with 18/5.

Solution:-

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎Here, as we're asked to state whether runner- A can beat runner- B, we can solve this problem easily, as we know the distance of the race and the time taken by runner- A. How can we find? The steps of finding are listed below:

• Finding the speed of Runner- A.
• Converting the speed (kmph) of Runner- B into m/s.
• Comparing the speed of both runners.

Let's start solving!

～ Speed of runner- A:

We know that,

$\: \: \: \: \: \: \: \: \boxed{ \sf{\pmb{Speed = \dfrac{Distance}{Time}} }}$

$\longmapsto{ \sf{Speed = \dfrac{75 \cancel{0}}{15 \cancel{0}} }} \\ \\ \longmapsto{ \sf{Speed = \dfrac{ \cancel{75}}{ \cancel{15}} }} \\ \\ \longmapsto \boxed{ \tt{ \pmb{ \purple{Speed=5 \: m/s}}}}$

～ Conversion of speed of runner- B into m/s:

Scroll up! In the description of concept of the question, the conversion of units of speed has been given, i.e,

$\: \: \: \: \: \boxed{ \sf{\pmb{Speed \: in \: m/s = \dfrac{5}{18} \times Speed } }}$

On substituting the measures,

$\longmapsto{ \sf{ \dfrac{5}{18} \times 17.95 }} \\ \\ \longmapsto{ \sf{ \dfrac{ \cancel{5}}{18} \times \frac{1795}{ \cancel{100}} }} \\ \\ \longmapsto { \sf{ \dfrac{1}{18} \times \dfrac{1795}{20} }} \\ \\ \longmapsto { \sf{ \dfrac{ \cancel{1795}}{ \cancel{360}} }} \\ \\ \longmapsto \boxed{ \tt { \pmb{ \purple{4.98 \: m/s}}}}$

～ Comparison of speeds of both the runners:

• Speed of runner- A = 5 m/s
• Speed of runner- B = 4.98 m/s

Since the speed of runner- A is greater than runner- B, i.e,

$\: \: \boxed{ \sf{Runner \: A _{ (speed)} > Runner\:B _{(speed)}}}$

Runner- A can beat Runner- B in the race.

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