The speed of a motorboat in still water and that of the current of water is in a ratio of 27 : 5. The boat goes along the current from point A to point B in 3 hours 40 minutes. How much time will it take to come back from B to A?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 5 hours 20 minutes
Speed of boat in still water : speed of stream $=27:5$
Let speed of boat in still water $=27k$ and speed of stream $=5k$
Speed downstream $=27k+5k=32k$
Speed upstream $=27k-5k=22k$
Time downstream $=3$ hours $40$ minutes $=\frac{11}{3}$ hours
Distance between $A$ and $B$
$=32k\times\frac{11}{3}=\frac{352k}{3}$
Time upstream
$=\frac{\text{distance}}{\text{speed upstream}}=\frac{\frac{352k}{3}}{22k}$
$=\frac{352}{66}=\frac{176}{33}$ hours
$=\frac{176}{33}$ hours $=5\frac{11}{33}$ hours
$=5$ hours $20$ minutes
The time taken to return from $B$ to $A$ is $5$ hours $20$ minutes.