Question

What is the greatest possible speed at which a man can walk 52 km and 91 km in an exact number of minutes.

Answer 1

Hint: To answer this type of problem we take HCF of both the speeds and get the greatest possible speed. The HCF of both numbers will be our required answer.

Complete step-by-step answer:
Given that a man can walk 52 km and 91 km in an exact number of minutes.
And we have to find the greatest possible speed for that.
We generally use HCF highest common factor concept to solve this type of problems
So HCF (52, 91) = greatest possible speed.
So we will find the prime factors of 52 first
 $ 52 = 2 \times 2 \times 13 $ …….…(i)
And prime factor of 91 are
 $ 91 = 7 \times 13 $ ………………(ii)
Now from equation I and equation ii the highest common factor is 13
 $ \Rightarrow $ Means the HCF of the 52 and 91 is 13
 $ \Rightarrow $ Means the greatest possible speed is equal to 13 km/h
Hence the greatest possible speed is 13 km/h

Note: Some time students get confused and take the LCM lowest common factor in place of HCF highest common factor. So while solving this type question students keep in mind these mistakes.