Question

edward can paddle his kayak 7 miles per hour in still water. it takes him the same time to paddle 12.5 miles upstream as it takes paddle him 22.5 miles downstream. determine the speed of the river’s current. a) using the variable c to represent the speed of the river’s current in miles per hour, write an equation using the information as it is given above that can be solved the problem. equation: b) how fast is the river’s current? miles per hour.

Explanation:

Part A

Step1: Determine upstream and downstream speeds

Upstream speed: \( 7 - c \) (since current opposes, subtract \( c \) from still - water speed)
Downstream speed: \( 7 + c \) (since current aids, add \( c \) to still - water speed)

Step2: Recall time formula (\( t=\frac{d}{s} \), where \( t \) is time, \( d \) is distance, \( s \) is speed)

Time upstream: \( \frac{12.5}{7 - c} \)
Time downstream: \( \frac{22.5}{7 + c} \)

Step3: Set times equal (same time for both trips)

\( \frac{12.5}{7 - c}=\frac{22.5}{7 + c} \)

Step1: Cross - multiply the equation from Part A

\( 12.5(7 + c)=22.5(7 - c) \)

Step2: Expand both sides

\( 87.5+12.5c = 157.5-22.5c \)

Step3: Add \( 22.5c \) to both sides

\( 87.5 + 12.5c+22.5c=157.5-22.5c + 22.5c \)
\( 87.5+35c=157.5 \)

Step4: Subtract 87.5 from both sides

\( 35c=157.5 - 87.5 \)
\( 35c = 70 \)

Step5: Divide both sides by 35

\( c=\frac{70}{35}=2 \)

Answer:

\(\frac{12.5}{7 - c}=\frac{22.5}{7 + c}\)

Part B