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Speed of boat by the time taken for a round trip in the river (running water)

ÀÛ¼ºÀÚ Uploader : billy ÀÛ¼ºÀÏ Upload Date: 2019-11-13º¯°æÀÏ Update Date: 2020-02-19Á¶È¸¼ö View : 1488

The distance between two upstream and downstream points of the river is L (km), the speed of the flowing water is Vr (m / s), and the time taken to shuttle back and forth is Th (hr), Tm (min), Ts (sec).  Then, the speed of boat V (m / s) can be obtained as follows.

Time taken up the river: Tu = 1000 * L / (V-Vr) (sec)
Time taken down the river: Td = 1000 * L / (V + Vr) (sec)
Time converted to seconds taken: T = 3600*Th + 60*Tm + Ts

Since T = Tu+Td,

T = 1000*L*(1/(V-Vr) + 1/(V+Vr))

2*V/(V^2-Vr^2) = T/(1000*L)

T/(2000*L)*V^2 - V - T/(2000*L)*Vr^2 = 0

V^2 - (2000*L)/T*V - Vr^2 = 0

V is solved by using the quadratic formula.

V = (1000*L)/(3600*Th+60*Tm+Ts)+((1000*L/(3600*Th+60*Tm+Ts))^2+Vr^2)^(1/2)

*** Âü°í¹®Çå[References] ***

V = (1000*L)/(3600*Th+60*Tm+Ts)+((1000*L/(3600*Th+60*Tm+Ts))^2+Vr^2)^(1/2)
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