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Rima is traveling in her car at the speed of 60 km/hr. She drops her hat and didn’t recognize it for 10 minutes, during this time the hat travels due to air drag. As soon as she recognizes this she turns her car around and drive 50% faster to get her favourite hat, so that she could get her hat after 15 minutes after the fall. Find the average speed of the hat with which it travelled till it was caught.

Rima is traveling in her car at the speed of 60 km/hr. She drops her hat and didn’t recognize it for 10 minutes, during this time the hat travels due to air drag. As soon as she recognizes this she turns her car around and drive 50% faster to get her favourite hat, so that she could get her hat after 15 minutes after the fall. Find the average speed of the hat with which it travelled till it was caught. Correct Answer 10 km/hr

Given:

Initial Speed of Rima = V­1­ = 60 km/hr

Total time to grab the hat = T = 15 minutes

Time till Rima recognize fall of her hat = T1 = 10 minutes

Speed of hat = x km/hr

Speed of Rima during chase = V2 = 60 × (100 + 50)/100

⇒ 60 × 3/2

⇒ 90 km/hr

Time of chase = T2 = T – T1

⇒ 15 – 10 = 5 minutes

Formula used :

Speed = Distance/ Time

Relative velocity (Objects running in same direction) = Va­ – Vb

Relative velocity (Objects running in opposite direction) = Va + V­b

Calculation :

Relative speed of cap till Rima notices drop = V1 – x

⇒ (60 – x) km/hr

Distance between Rima and hat = (60 – x) × 10/60

⇒ (60 – x)/6

Relative speed of Rima while chasing = V2 + x

⇒ (90 + x) km/hr

(60 – x)/6 is covered by Rima with relative velocity in 5 minutes.

⇒ (90 + x) × 5/60 = (60 – x)/6

⇒ (90 + x) × 1/2 = (60 – x)

⇒ 90 + x = 120 – 2x

⇒ 3x = 30

⇒ x = 10 km/hr

∴ The hat travelled with the average speed of 10 km/hr till it was caught.

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