Part 1 What's their speed? You are going to calculate what speed the kayakers are paddling, If they stay at a constant rate the entire trip, while kayaking in Humboldt bay. Watch this video and write down the key Information needed to solve the problem D Kayak Part 1 Question KAYAK TRIP DOWN HUMBOLDT CHANNEL 0:01 /2:19 Ke Youtube C3 " )Write down the key Information from the video 2) Draw a picture to model the problem 3) Label variables and create a table 4) Write an equation to model the problem 5) Solve the equation. Provide supporting work and detail 6) Explain the resultsPart 2: How far can you travel? Apparently, the length of your kayak affects the speed your kayak can travel. Based on the table below, choose a kayak length. Maximum Speed Table Waterline Length Miles Per (Feet) Knots Hour 9 4.0 4.6 10 4.2 4.9 11 4.4 5.1 12 4.6 5.3 13 4.8 5.6 14 5.0 5.8 15 5.2 6.0 16 5.4 6.2 17 5.5 6.4 18 5.7 6.5 1) What kayak size are you picking? 2) Using the information you picked, if you travel at maximum speed upstream with a river current of 2 miles per hour, find how far it will take you to travel in 6 hours? A) First, draw a picture to depict the situation. Identify the variables and write an equation to solve for the distance. B) Solve the equation and show your work.Example: River Cruise A 3 hour river cruise goes 15 km upstream and then back again. The river has a current of 2 km an hour. What is the boat's speed and how long was the upstream journey? There are two speeds to think about: the speed the boat makes in the water, and the speed relative to the land: Let x = the boat's speed in the water (lanyh) Let v = the speed relative to the land (km/h) Because the river flows downstream at 2 kmy/h: when going upstream, v . x-2 (its speed is reduced by 2 kmyth) when going downstream, v = >+2 (its speed is increased by 2 kmyh) We can turn those speeds into times using: time = distance / speed (to travel 8 kon at 4 kow/h takes 8/4 = 2 hours, right?) And we know the total time is ] hours: total time = time upstream + time downstream = 3 hours Put all that together: total time = 15/(x-2) + 15/(x+2) = 3 hours Now we use our algebra skills to solve for "%". First, get rid of the fractions by multiplying through by (x-2](x+2]: 3(x-2)(x+2) = 15(x+2) + 15(x-2) Expand everything: 3(x -4) = 15x+30 + 15x-30 Bring everything to the left and simplify: 3x7- 30x - 12 = 0 It is a Quadratic Equation! Let us solve it using the Quadratic Formula X =. -b+,b2- 4ac 2a Where a, b and e are from the Quadratic Equation in "Standard Form": ax + bx + c= 0 Solve 3x3 - 30x - 12 = 0 Coefficients are: a = 3, b = -30 and c = -12 Quadratic Formula: x = [-b = v(b]-4ac) ]/ 2a Put in a, band c: x = [-(-30) . v([-30)3-4x3x(-12)) ]/ (2x3) Solve: * = [ 30 = v(900+144) ]/6 x = [ 30 = V(1044) 1/ 6 x = (30 # 32.31 ) / 6 x-0.39 or 10.39 Answer x = =0.39 or 10.39 (to 2 decimal places)