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Two cyclists start simultaneously from two points A and B, their destinations being B and A, respectively. After crossing each other; they precisely take 2 hours 33 minutes 36 seconds and 1 hour 26 minutes 24 seconds respectively to reach their destinations. What is the ratio of the speed of the first to that of the second cyclist?

Two cyclists start simultaneously from two points A and B, their destinations being B and A, respectively. After crossing each other; they precisely take 2 hours 33 minutes 36 seconds and 1 hour 26 minutes 24 seconds respectively to reach their destinations. What is the ratio of the speed of the first to that of the second cyclist? Correct Answer 3 ∶ 4

Given:

Two cyclists travel equal distances from points A and B.

Concept Used:

When distance is the same then speed is inversely proportional to the time.

Note: 
If after crossing each other they take x and y time to reach their destinations then,

Speed1/Speed2 = √(T2/T1)

1 hour = 60 min

1 min = 60 sec

Calculation:

According to the question

Time is taken by first after crossing, T1 = 2 hours 33 min 36 sec

⇒ (2 × 3600 + 33 × 60 + 36) sec

⇒ (7200 + 1980 + 36) = 9216 sec

Time is taken by second after crossing, T2 = 1 hour 26 min 24 sec

⇒ (1 × 3600 + 26 × 60 + 24) sec

⇒ 3600 + 1560 + 24) = 5184 sec

Now,

⇒ Speed of first, (s1)/speed of second, (s2) = √(T2/T1)

⇒ √(5184/9216)

⇒ √(324/576) = 18/24

⇒ s1 : s2 = 18 : 24

⇒ 3 : 4

 ∴ The ratio of the speed of the first to that of the second cyclist is 3 : 4 .

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