Question

While Brendan is vacationing with his family at the cabin, they take a motorboat on the river. The motorboat travels 18 miles per hour in still water.

a. Let w represent the speed of the river current in miles per hour. Write an expression for how fast the motorboat is able to go downstream (with the current) Write another expression for how fast the motorboat is able to go upstream (against the current).
b. The motorboat travels 49 miles upstream in the same time it takes to travel 77 miles downstream. What is the speed of the current w? Use the Elimination Method to solve.
c. Could you have used the Equal Values Method or the Substitution Method to solve this problem? Explain. (You do not actually solve using these two methods.)​

Answer 1

The speed of the motorboat going downstream is 18 + w, and the speed going upstream is 18 - w. To find the speed of the current w, set up an equation using the given distances and solve using the elimination method. The Equal Values Method or the Substitution Method could also be used to solve this problem.

Step-by-step explanation:

a. The speed of the motorboat going downstream (with the current) can be represented as the sum of the speed of the boat in still water and the speed of the river current. So the expression for this speed is 18 + w, where w is the speed of the river current in miles per hour. The speed of the motorboat going upstream (against the current) can be represented as the difference between the speed of the boat in still water and the speed of the river current. So the expression for this speed is 18 - w.

b. To solve for the speed of the current w, we know that the time it takes to travel upstream and downstream is the same. So we can set up the equation: 49 / (18 - w) = 77 / (18 + w). We can then use the elimination method to solve for w.

c. The Equal Values Method or the Substitution Method could also be used to solve this problem. With the Equal Values Method, we would set the expressions for the speed downstream and upstream equal to each other: 18 + w = 18 - w. With the Substitution Method, we would solve one of the expressions for w and substitute it into the other expression.