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A driver travels three-fourth distance of his journey at a velocity (v) and completes...

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saj-94 | Salutatorian

Posted August 20, 2013 at 3:23 PM via web

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A driver travels three-fourth distance of his journey at a velocity (v) and completes rest of the journey at one half of his original velocity (½v). What was his average speed for the trip?
 
[1] 0.85v 

[2] 0.80v     

[3] 0.75v 

[4] 0.70v 

[5] 0.65v

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted August 20, 2013 at 3:32 PM (Answer #1)

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Let us say the total travel distance is D.

So then `3/4D ` of the distance is travelled under velocity v and the rest `1/4D` is travelled under velocity `1/2v` .

Time for travel at `v` speed `(t_1) = (3/4D)/v = (3D)/(4v)`

Time for travel under `1/2v` speed` (t_2 ) ` `= (1/4D)/(1/2v) = D/(2v)`

Average speed = (total distance)/(total time)

Average speed `= D/(t_1+t_2)`

Average speed `= D/((3D)/(4v)+D/(2v))`

Average speed `= D/((5D)/(4v))`

Average speed `= 4/5v`

Average speed `= 0.8v`

So the answer is 0.8v. The correct answer is at [2].

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