Question

If a boat travels from Town A to Town B, it has to travel 630mi along a river. A boat traveled from Town A to Town B along the river's current with its engine running at full speed. This trip took 31.5hr. Then the boat traveled back from Town B to Town A, again with the engine at full speed, but this time against the river's current. This trip took 45hr. Write and solve a system of equations to answer the following questions. The boat's speed in still water with the engine running at full speed is The river current's speed was Use mi for miles, and hr for hours.

Answer 1

The system of equations is set up with two variables representing the boat's speed in still water (b) and the river current's speed (c). By solving the system, we determine that the boat's speed in still water is 17 mi/hr and the river current's speed is 3 mi/hr.

Step-by-step explanation:

To find the boat's speed in still water and the river current's speed, we set up two equations based on the information given. Let b be the boat's speed in still water and c be the river current's speed. When traveling downstream, the boat's effective speed is (b + c) and the total distance divided by this speed gives us the time it takes to travel from Town A to Town B. Hence, the first equation based on downstream travel is (b + c) * 31.5 = 630.

When traveling upstream, against the current, the boat's effective speed is (b - c). Using the time it takes to travel back from Town B to Town A, which is 45 hours, we set up the second equation: (b - c) * 45 = 630.

Now we solve the system of equations:

• b + c = 630 / 31.5
• b - c = 630 / 45
• Solving these two equations, we can find the values of b and c.
• Equation 1 simplifies to b + c = 20
• Equation 2 simplifies to b - c = 14
• Adding both equations, we get 2b = 34, so b = 17 mi/hr. This means the boat's speed in still water is 17 miles per hour.
• Substituting b = 17 in one of the equations to solve for c, we find c = 3 mi/hr. Thus, the river current's speed was 3 miles per hour.