A paddle boat can move at a speed of 20 ​km/h in still water. The boat is paddled 6 km downstream in a river in the same time it takes to go 3 km upstream. What is the speed of the​ river?

1 Answer
BillytheKid
Nov 14, 2017

OK, let's try this...

Explanation:

In kinematics:
#x_t = v_0 . t + x_0#
#x_0# (startpoint) is not important here, so:

#x_t = v_0 . t#;

#x_"out" = 6 km#;
#x_"back" = 3 km#;
#t_"out"= t_"back"#;
#v_"out"= v_"boat" + v_"river"#;
#v_"back"= v_"boat" - v_"river"#;

#rarr # #x_"out" = 2x_"back"#;
#rarr # #v_"out".t = 2v_"back" . t#;

Divide by t, as this is same for outgoing and return,
#rarr v_"out" = 2v_"back" #;

#v_"out" = v_"boat" + v_"river" #;
#v_"back " = v_"boat" - v_"river" #;

#rarr v_"boat" + v_"river" = 2(v_"boat" - v_"river")#
#rarr v_"boat" + v_"river" = 2v_"boat" - 2v_"river"#
#rarr v_"river" = v_"boat" - 2v_"river"#
#rarr 3v_"river" = v_"boat" #
#rarr v_"river" = v_"boat" /3#

#v_"boat" = 20 "km/hr", rarr v_"river"= 20/3 = 6 2/3# km/hr....

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