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A person goes from point A to B and comes back. His average speed for the whole journey is 65 km/hr. If his speed while coming back from B to A is 40 km/hr, then what will be the speed of the person (in km/hr) while going from A to B?

A person goes from point A to B and comes back. His average speed for the whole journey is 65 km/hr. If his speed while coming back from B to A is 40 km/hr, then what will be the speed of the person (in km/hr) while going from A to B? Correct Answer 173.33

Let,

The distance from point A to B is = x km

Speed of the person (in km/hr) while going from A to B = y km/h

∴ Time taken to go B from A = distance covered/speed = x/y hours

Speed while coming back from B to A is 40 km/hr

∴ Time taken to go B from A = distance covered/speed = x/40 hours

∴ Total time to go from point A to B and comes back

= Time taken to go A from B + Time taken to go B from A

= (x/y + x/40) hours

Average speed = (Total distance covered/Total time taken) = 2x/(x/y + x/40) = 2/(1/y + 1/40)

= 80y/(40 + y)

Given,

Average speed = 65 km/hr

80y/(40 + y) = 65

⇒ 80y = 2600 + 65y

⇒ 15y = 2600

⇒ y = 173.33 km/h

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