Homework 9.5 Solve Applications of Quadratic Equations

Question

A boat makes a round trip journey to and from an island that is 220 meters from shore. In still water, the boat's motor propels the boat at a speed of 5 meters per second, but a current flows directly towards the island which affects the boat's speed. If the round trip journey takes 10 minutes (600 seconds), what is the speed of the current?

Let r denote the speed of the current. Use the relation

distance = rate × time,

to write an expression for the time it takes the boat to reach the island in terms of r.

  

Write an expression for the time it takes the boat to return from the island in terms of r.

  

Using the fact that the sum of these two times is 10 minutes, find the speed of the current.

( m/s )

Answer 1

To reach the island takes a short time d/(s + r) because the current adds to the boat speed. To return takes a longer time d/(s – r) because the current subtracts from the boat speed. Now solve the total time for r: t = d/(s + r) + d/(s – r) = 2ds/(s² – r²), that is r = √(s² – 2ds/t) = √(5² – 2×220×5/600) = 4.62 m/s.

Answer 2

a) t₁ =220/(r+5)

b) t₂=220/(r-5)

c) t₁+t₂= 220/(r+5) + 220/(r-5) = 600

600r²-440r -15000 =0

Divide thru by 40

15r²-11r-375=0

Use the quadratic equation to solve for r and take the positive value.