Question

Manpreet took part in an inter school race competition. He cycled 2.7 km, ran for \[\dfrac{2}{3}\] hours and walked the remaining 500m of the race. If the total distance of the race was 12km, then find her running speed.
(a) 13.2 km/hr
(b) 12 km/hr
(c) 7.5 km/hr
(d) 8.8 km/hr

Answer 1

Hint: To solve this question, we will assume the variables for all the given distances and then try to find the distance of her running duration. This can be obtained as the total distance if the race is given as 12 km. After calculating the distance of running, we will calculate the speed of it by using the formula, \[\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}\] where time is already given.

Complete step by step answer:
Given that Manpreet cycled for 2.7 km. Let this be assumed as a variable x.
\[x=2.7km\]
We are given that she ran for \[\dfrac{2}{3}\] hours. Let this time be represented as t.
\[t=\dfrac{2}{3}hr\]
Let the distance she travelled by running be represented as y. So, to travel a distance y km, she took \[t=\dfrac{2}{3}hr.\] Finally, she walked the remaining 500m of the race. Let it be represented by z.
\[z=500m\]
Now, the total distance of the race is 12km.
\[\Rightarrow x+y+z=12km\]
Observer that x = 2.7km, y is not known and z = 500m = 0.5 km.
As by using the unitary method, we have,
\[1km=1000m\]
\[\Rightarrow 1000m=1km\]
\[\Rightarrow 1m=\dfrac{1}{1000}km\]
\[\Rightarrow 500m=\dfrac{1}{1000}\times 500km\]
\[\Rightarrow 500m=0.5km\]
So, z = 0.5.
\[\Rightarrow x+y+z=12km\]
\[\Rightarrow 2.7+y+0.5=12km\]
\[\Rightarrow 3.2+y=12km\]
\[\Rightarrow y=12-3.2\]
\[\Rightarrow y=8.8\]
So, the distance y = 8.8km.
Hence, she ran for 8.8.km in time, \[t=\dfrac{2}{3}hr.\]
Finally, we have to calculate the running speed. To do so, we will use the formula,
\[\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}\]
Using this, we have,
Distance = y = 8.8km
\[t=\dfrac{2}{3}hr=0.6667\]
\[\Rightarrow \text{Speed}=\dfrac{8.8}{0.6667}\]
\[\Rightarrow \text{Speed}=13.199\]
\[\Rightarrow \text{Speed}\approx 13.20\]
\[\Rightarrow \text{Speed}=13.20\]
So, the speed of Manpreet running is 13.20 km/hr.

So, the correct answer is “Option A”.

Note: A possibility of a mistake in this question is that the student might not convert the distance given as 500m into km. Always in such types of questions, change all the given values to a single unit and then proceed. Here, we have to change 500m into km. We can also change all the values into m and then we would change time in seconds and not in hours. This step is correct but it is not required as the answer itself is given in km/hr.