Roy kayaked up and down a river and a total of 7 hours. His trip was 5 miles each way. If Roy kayaked at a speed of 6 mph what was the speed of the current?

Answer 1

distance = rate * time

distance/rate = time

time upstream + time downstream = 7

5/ (6-x) + 5/(6+x) = 7

5(6+x) + 5(6-x) = 7(36 - x^2)

30 + 5x + 30 - 5x = 252 - 7x^2

60 = 252 - 7x^2

-192 = -7x^2

-192/-7 = x^2

192/7 = x^2

sqrt(192)/sqrt(7) = x

sqrt(2 * 96)/ sqrt(7) = x

sqrt(2*2*2*2*2*2*3)/ sqrt(7) = x

8 * sqrt(3)/ sqrt(7) = x

8 * sqrt(21)/ 7 = x

x=(8/7)*sqrt(21)

check:

the times are:

5/[6 + (8/7)*sqrt(21)] = 5*[ 6 - (8/7)*sqrt(21)] / [ 36 - (64/49)*21 ]

= 5 * [ 6 - (8/7)sqrt(21)] / [ 36 - 64*3/7 ]

= 35 * [ 6 - (8/7)sqrt(21)]/ [ 36*7 - 64*3]

5/[6 - (8/7)*sqrt(21)] = 35 * [ 6 + (8/7)sqrt(21)]/ [ 36*7 - 64*3]

adding these together.... 35*6 = 210... this gets doubled , so 420

(8/7)sqrt(21) cancels out

meanwhile the denominator is 60

420/60 = 7

yes it checks

2