A kayak can travel 30 miles downstream in 2 ​hours, while it would take 10 hours to make the same trip upstream. Find the speed of the kayak in still​ water, as well as the speed of the current

Question

Things did not go quite as planned. You invested

​$18,640​,

part of it in a stock that paid​ 12% annual interest.​ However, the rest of the money suffered a​ 5% loss. If the total annual income from both investments was

​$1992​,

how much was invested at each​ rate?

Answer 1

30 = (R+S)*2 = 2R + 2S

30 = (R-s)*10 = 10R - 10S

8R - 12S = 0

8R = 12S

R = (3/2)S

30 = 2*(3/2)S + 2S = 3S + 2S = 5S

S = 6

R = 9

The speed of the kayak is 9 mph while the speed of the boat is 6 mph

30/(9+6) = 30/15 = 2 going downstream with the current while

30/(9-6) = 30/3 = 10 going upstream against the current