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When a man travels equal distance at speed $x km / h$ and $y km / h$ , his average speed is $4 km / h$ . But when he travels at these speed for equal time, his average speed is $4.5 km / h$ . The difference of the two speed is

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answer is D.

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Detailed Solution

Given that, a man travels equal distance at speed

x km / h

and

y km / h

, his average speed is

4 km / h

.
Average speed = Distance travel / time
Let, man speeds be x and y, then

d d x + d y = 4 x t + y t 2 t = 4.5 x y x + y = 4 Or, x + y 2 = 4.5 Or, x + y = 9 and x y = 36 ∴ x − y = (x + y) 2 − 2 x y = 81 − 72 = 3

Therefore, the difference between the two speeds is 3.
Hence, option (4) is correct.

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