MathematicsWhat is the greatest possible speed at which a man can walk 52 km and 91 km ?

What is the greatest possible speed at which a man can walk $52 km$ and $91 km$ ?

A
17 km/ hour
B
7 km/hour
C
13 km/hour
D
26 km/hour

Solution:

Given that a man can walk 52 km and 91 km.
To find the greatest possible speed at which a man can walk 52 km and 91 km in an exact number of minutes, it is required to find the HCF of 52 and 91.
Thus, the prime factorization of 52 and 91 is

⇒ 52 = 2 × 2 × 13 ⇒ 91 = 7 × 13

So,

H C F 52, 91 = 13

.
Therefore, the greatest possible speed at which a man can walk 52 km and 91 km in an exact number of minutes is 13 km/ hour.
Hence the correct answer is option (3).