Jake went on a riverboat tour. after returning from the tour, he was curious to know the speed at which the boat was going. during the tour, he was told that he would travel 10 miles upstream and then 10 miles downstream. he also knows that the river was flowing at a rate of 3 miles/hour and that the tour took about three hours.
the boat moved at a constant speed for the whole journey, although its actual speed varied with the current.
jake wants to know the boat’s actual speed going upstream and actual speed coming downstream. if the boat was moving at a constant speed of x miles per hour, determine the boat’s relative speed in each direction.
was the time it took the boat to go upstream the same as the time it took to come downstream?
jake first reasoned that because the boat ride took 3 hours, it must have taken 1.5 hours to go upstream and 1.5 hours to go downstream. thinking about it further, however, he realized that the ride upstream had to take longer than the trip downstream. what is the reason it took longer to travel one direction than the other?
the time it took the boat to go upstream is u, and the time it took to come downstream is d. what is u + d?
type your response here:
jake knows that the relationship between distance (d), velocity (v), and time taken (t) is given by d = vt. rewrite this equation for t.
using the equation you rewrote in part e, write an equation for the time taken for the upstream trip.
now construct an equation for the time taken for the downstream trip.
jake already has the equation u + d = 3, which represents the total time taken for the whole journey. now that he has individual equations for u and d, he needs to combine these three equations to get a single equation. construct a combined equation for u + d in terms of x, the constant speed at which the boat was going.
jake now has an equation with x as the only unknown variable. he needs to solve for x. transform the equation you found in part h into a quadratic equation, and find the value of x, the constant speed at which the boat traveled.