Discussion
The time taken by a boat to go 21 km downstream is equal to the time taken by it to go 9 km upstream. To go 12 km downstream and the same distance upstream, it takes a total of \(5\frac{5}{7}\) hours. How much time (in hours) will the boat take to go 28 km downstream?
Answer: C
The boat takes 4 hours to go 28 km downstream. Equal times for 21 km downstream and 9 km upstream mean the speeds are in the ratio 21 : 9 = 7 : 3, so downstream speed is \(7k\) and upstream speed is \(3k\). \[ \begin{aligned} \frac{12}{7k} + \frac{12}{3k} &= 5\frac{5}{7} \\ &= \frac{40}{7} \end{aligned} \] \[ \begin{aligned} \frac{12 + 28}{7k} &= \frac{40}{7k} \\ &= \frac{40}{7} \Rightarrow k \\ &= 1 \end{aligned} \] Downstream speed is 7 km/h, so \[ \frac{28}{7} = 4\text{ hours} \] The other options do not match this speed.
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