Question

A & B are two towns. A person covers the distance from A to B on cycle at 17kmph and returns to A by a boat running at a uniform speed of 8kmph. His average speed for the whole journey is 

A.    12.5 km/h


B.    12.33 km/h


C.    10.75 km/h


D.    10.88 km/h

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Answer 1

Answer : D.

When same distance is covered with different speeds, then the average speed = 2xy / x+y = 10.88kmph

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Answer 2

Answer:

His average speed for the whole journey = = 10.88km/h

The correct answer is option (D) 10.88km/h

Step-by-step explanation:

Given,

Speed of the person from A to B by cycle = 17km/h

Speed of the person from B to A by boat = 8km/h

To find,

The average speed for the whole journey

Solution:

Recall the formula

Distance traveled = speed × time taken

Average speed = $\frac{Total \ distance }{Total \ time \ taken}$

Let 'd' be the distance between A and B

Then the total distance traveled by the person = d+d = 2d

Time taken to travel from A to B = $\frac{distance }{speed} = \frac{d}{17}$

Time taken to travel from B to A = $\frac{d}{8}$

Total time taken by the person to travel both the journey = $\frac{d}{17} + \frac{d}{8}$

= $\frac{8d+17d}{8X17}$

= $\frac{25d}{8X17}$

= $\frac{25d}{136}$

Total time taken = = $\frac{25d}{136}$

Average speed = $\frac{Total \ distance }{Total \ time \ taken}$ = $\frac{2d}{\frac{25d}{136} }$

= $\frac{2X136}{25}$

= 10.88km/h

∴His average speed for the whole journey = = 10.88km/h

The correct answer is option (D) 10.88km/h

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