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Two rabbits start running towards each other, one from A to B and another from B to A. They cross each other after one hour and the first rabbit reaches B, 5/6 hour before the second rabbit reaches A. If the distance between A and B is 50 km, what is the speed of the slower rabbit?

Two rabbits start running towards each other, one from A to B and another from B to A. They cross each other after one hour and the first rabbit reaches B, 5/6 hour before the second rabbit reaches A. If the distance between A and B is 50 km, what is the speed of the slower rabbit? Correct Answer 20 km/h

Given:

Two rabbits start running towards each other, one form A to B and another from B to A.

They cross each other after one hour and the first rabbit reaches B, 5/6 hour before the second rabbit reaches A

Distance between A and B = 50 km

Formula:

Speed = distance/time

Calculation:

Let the speed of slower rabbit and faster rabbit be x km/hr and y km/hr respectively.

According to the question

x + y = 50/1

⇒ x + y = 50      --- (1)

Again,

50/x – 50/y = 5/6     --- (2)

From (1) and (2), we get

50/x – 50/(50 – x) = 5/6

⇒ 60 (50 – x – x) = x (50 – x)

⇒ 3000 – 120x = 50x – x2

⇒ x2 – 170x + 3000 = 0

⇒ (x – 150) (x – 20) = 0

⇒ x = 20 (∵ x = 150 not possible)

∴ Speed of slower rabbit is 20 km/hr.

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