Question

A boat travels 140 miles downstream in the same amount of time as it takes to travel 92 miles upstream. The speed of the current is 6 mph. What is the speed of the boat?

Answer 1

To solve the problem, we will use the relationship between speed, distance, and time.

Let \( b \) be the speed of the boat in still water (in mph). The speed of the current is given as 6 mph.

### Downstream:
When traveling downstream, the effective speed of the boat is:
\[
b + 6
\]
The distance traveled downstream is 140 miles, so the time taken to travel downstream (\( t_{down} \)) can be expressed as:
\[
t_{down} = \frac{140}{b + 6}
\]

### Upstream:
When traveling upstream, the effective speed of the boat is:
\[
b - 6
\]
The distance traveled upstream is 92 miles, so the time taken to travel upstream (\( t_{up} \)) can be expressed as:
\[
t_{up} = \frac{92}{b - 6}
\]

### Setting the times equal:
According to the problem statement, the time taken downstream is equal to the time taken upstream:
\[
\frac{140}{b + 6} = \frac{92}{b - 6}
\]

### Cross-multiplying to solve for \( b \):
Cross-multiplying gives us:
\[
140(b - 6) = 92(b + 6)
\]

Expanding both sides:
\[
140b - 840 = 92b + 552
\]

Rearranging the equation to isolate \( b \):
\[
140b - 92b = 552 + 840
\]
\[
48b = 1392
\]

Now, dividing both sides by 48:
\[
b = \frac{1392}{48} = 29
\]

### Conclusion:
The speed of the boat in still water is \( \boxed{29} \) mph.