Question

A hare and a tortoise run between points O and P located exactly 6 km from each other on a straight line. They start together at O, go straight to P and then return to O along the same line. They run at constant speeds of 12 km/hr and 1 km/hr respectively. Since the tortoise is slower than the hare, the hare shuttles between O and P until the tortoise goes once to P and returns to O. During the run, how many times are the hare and the tortoise separated by an exact distance of 1 km from each oth

Accepted Answer

E. Total distance for tortoise = $6 + 6 = 12$ km. At speed 1 km/hr, total time = 12 hours. Hare speed = 12 km/hr, so total distance = $12 	imes 12 = 144$ km = 12 complete rounds of $O 	o P 	o O$. In each round of the hare (12 rounds total): - Round 1: 3 occurrences of 1 km separation. - Rounds 2 to 5: 4 occurrences each $\implies 4 	imes 4 = 16$. - Round 6: 2 occurrences. First half = $3 + 16 + 1 = 20$ occurrences. By symmetry, the second half (rounds 7 to 12) has another 20 occurrences. Total occurrences = $20 	imes 2 = 40$.

Hare and Tortoise Race Separations

Explanation

Practise this under exam conditions