A boat traveled 336 miles downstream and back. The trip downstream took 12 hours. The trip back took 14 hours. What is the speed of the boat in still water? What is the speed of the current?

1 Answer
A08
Jan 20, 2016

Speed of boat in still water #=26 #miles# //hour#
Speed of the current #=2 #miles# //hour#

Explanation:

Let #v_B# be the speed of boat in still water, and #v_C# be the speed of the current.
Relative speed of the boat downstream is #=v_B+v_C#
and Relative speed of the boat upstream is #=v_B-v_C#

Using the relation #"distance" = "speed" times "time#

For Downstream Journey
#336=(v_B+v_C)times 12#
#implies (v_B+v_C)=336/12=28#...................(1)

For Upstream Journey
#336=(v_B-v_C)times 14#
#implies (v_B-v_C)=336/14=24#....................(2)

Adding equations (1) and (2)
#2v_B=28+24#
Gives #v_B=26 #miles# //hour#

Substituting this value in either of the two equations we obtain
#v_C=2 #miles# //hour#

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