Question

haji rows his canoe 10 mph in still water. he noticed one day that he could row 4 miles upstream in the same amount of time he could row 6 miles downstream. what was the approximate speed of the current that day? 5.0 mph 2.0 mph 10.0 mph 3.3 mph

Explanation:

Step1: Define Variables

Let \( c \) be the speed of the current (in mph). The speed upstream is \( 10 - c \) (since current opposes), and downstream is \( 10 + c \) (current aids). Time \( t \) is distance over speed, so \( t_{\text{up}}=\frac{4}{10 - c} \) and \( t_{\text{down}}=\frac{6}{10 + c} \). Given \( t_{\text{up}} = t_{\text{down}} \), set \( \frac{4}{10 - c}=\frac{6}{10 + c} \).

Step2: Solve the Equation

Cross - multiply: \( 4(10 + c)=6(10 - c) \). Expand: \( 40 + 4c = 60 - 6c \). Add \( 6c \) to both sides: \( 40+10c = 60 \). Subtract 40: \( 10c = 20 \). Divide by 10: \( c = 2 \).

Answer:

2.0 mph