A man can row at a speed of 5 km/hr in still water. If he rows a certain distance upstream and back to the starting point in a river which flows at 1.5 km/hr, what is his average speed for the double journey?

A. 3.5 km/h
B. 4.55 km/h
C. 5 km/h
D. 5.5 km/h
E. 6.5 km/h
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Speed upstream = 5-1.5=3.5 as 1.5 km/hr is against the man's speed and speed downstream = 5+1.5km/hr=6.5 when the speed of river assists the man.
A direct formula here - \(\frac{2ab}{a+b}\)=\(\frac{2*3.5*6.5}{3.5+6.5}=\frac{7*6.5}{10}=4.55km/h\)
This is called harmonic mean and should be used when one travels half distance at speed a and other half at speed b for a return trip or equal distances.

Otherwise, the method if you do not know the formula..
upstream = 3.5 and downstream = 6.5..
Take the distance as x or say LCM of 35 and 65 = 35*13 km

total time for the trip = \(\frac{35*13}{3.5}+\frac{35*13}{6.5}=130+70=200\) and total distance = 2*35*13=70*13=910.
average speed \(\frac{910}{200}=4.55\)
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