Two people paddle a canoe in a river flowing at a rate of 3 miles per hour, then they returned traveling upstream. The entire trip was 96 miles and the trip upstream took twice as long as the trip downstream. How fast did they row in still water? How many hours was the complete trip?

72

Step-by-step explanation:

speed in still water = 9 mph

total time = 12 hours

Step-by-step explanation:

speed = distance/time

distance = speed * time

Traveling downstream:

speed of river = 3 mph

speed of canoe in still water = v

speed of canoe going downstream = v + 3

distance = 96/2 = 48

time = t

distance = speed * time

48 = (v + 3)(t)

Traveling upstream:

speed of river = 3 mph

speed of canoe in still water = v

speed of canoe going downstream = v - 3

distance = 96/2 = 48

time = 2t

distance = speed * time

48 - d = (v - 3)(2t)

48 = (v + 3)(t)

48 = (v - 3)(2t)

vt + 3t = 48

2vt - 6t = 48

     -2vt - 6t = -96

(+)   2vt - 6t = 48

           -12t = -48

t = 4

vt + 3t = 48

4v + 3(4) = 48

4v + 12 = 48

4v = 36

v = 9

speed in still water = v = 9 mph

total time = t + 2t = 3t = 3(4) = 12 hours

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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