in her kayak bunny can travel 70 miles downstream with the current in 5 hours. the return trip against the current takes 7 hours. find the speed of the kayak in Stillwater and the speed of the current​

9514 1404 393

Step-by-step explanation:

Bunny's rate downstream is ...

  (70 mi)/(5 h) = 14 mi/h = k + c

Bunny's rate upstream is ...

  (70 mi)/(7 h) = 10 mi/h = k -c

The kayak speed is the average of these:

  (14 mi/h +10 mi/h)/2 = ((k +c) +(k -c))/2

  (24 mi/h)/2 = 2k/2

  12 mi/h = k

Then the current speed is ...

  c = k -10 = 12 -10 = 2 . . . . mi/h

The still-water speed of the kayak is 12 mi/h; the speed of the current is 2 mi/h.

Additional comment

World-class kayak paddlers will not maintain a speed more than 8 mi/h for that distance and/or time (140 miles in 12 hours). Bunny is exceptional.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

a c

step-by-step explanation: