Questions: Don Williams uses his small motorboat to go 3 miles upstream to his favorite fishing spot. Against the current, the trip takes 3/4 hour. With the current the trip takes 1/4 hour. How fast can the boat travel in still water? What is the speed of the current? In still water the boats speed is mph. The speed of the current is mph.

Solution Steps

To solve this problem, we need to set up equations based on the relationship between distance, speed, and time. Let \( b \) be the speed of the boat in still water and \( c \) be the speed of the current. When going upstream, the effective speed is \( b - c \), and when going downstream, it is \( b + c \). Using the given times and distances, we can set up two equations and solve for \( b \) and \( c \).

To find the speed of the boat in still water and the speed of the current, we define:

• \( b \) as the speed of the boat in still water (mph).
• \( c \) as the speed of the current (mph).

Given:

• Distance upstream and downstream: \( 3 \) miles.
• Time taken upstream: \( \frac{3}{4} \) hour.
• Time taken downstream: \( \frac{1}{4} \) hour.

The effective speed upstream is \( b - c \) and downstream is \( b + c \).

Using the formula \( \text{speed} = \frac{\text{distance}}{\text{time}} \), we set up the following equations:

• Upstream: \( \frac{3}{0.75} = b - c \)
• Downstream: \( \frac{3}{0.25} = b + c \)

Simplifying these equations, we get:

• \( 4 = b - c \)
• \( 12 = b + c \)

We solve the system of equations:

1. \( b - c = 4 \)
2. \( b + c = 12 \)

Adding these equations, we find: \[ 2b = 16 \] \[ b = 8 \]

Substituting \( b = 8 \) into the first equation: \[ 8 - c = 4 \] \[ c = 4 \]

Final Answer