Discussion
Guddi’s swimming speed in still water to the speed of river is 7:1. She swims 4.2 km up the river in just 14 min. How much time will Guddi take to swim 18.4 km down the river?
Answer: A
Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
Put \( b = 7k \) and \( r = k \), so
\[ b - r = 6k, \qquad b + r = 8k \]
From the upstream trip, with 14 min = \( \tfrac{7}{30} \) h:
\[ 6k = \frac{4.2}{7/30} = 18 \quad\Longrightarrow\quad k = 3 \]
\[ b + r = 8 \times 3 = 24 \text{ km/h} \]
\[ t = \frac{18.4}{24} = \frac{23}{30} \text{ h} = 46 \text{ minutes} \]
Setting the ratio up with a single unknown \( k \) is what turns two unknowns into one.
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