A boatman goes 80 km upstream and then 80 km back downstream in a total of 6 hours. The time he takes to go 5 km downstream is equal to the time he takes to go 4 km upstream. Find the speed of the boat in still water (in km/hr).
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 27
Distances covered in the same time are in the ratio of the speeds, so downstream speed : upstream speed \(=5:4\). The 6-hour trip then fixes the actual speeds.
Let the downstream speed be \(5k\) and the upstream speed \(4k\) km/hr
\(\displaystyle \frac{80}{4k}+\frac{80}{5k}=6\)
\(\displaystyle \frac{20}{k}+\frac{16}{k}=\frac{36}{k}=6\), so \(k=6\)
Downstream speed \(=30\) km/hr, upstream speed \(=24\) km/hr
Speed in still water \(\displaystyle =\frac{30+24}{2}=27\) km/hr
Why the other options are incorrect
Option (1) 3 — Incorrect. This is the speed of the current, \(\frac{30-24}{2}\), not of the boat.
Option (2) 20 — Incorrect. At 20 km/hr the 5 : 4 ratio needs a current of \(\frac{20}{9}\) km/hr, and the trip then takes 8.1 hours, not 6.
Option (3) 26 — Incorrect. At 26 km/hr the 5 : 4 ratio needs a current of \(\frac{26}{9}\) km/hr, and the trip then takes about 6.2 hours, not 6.