| A boat travels upstream from P to Q and downstream from Q to P in 3 h. If the speed of the boat in still water is 9 km/h and the speed of the current is 3 km/h, then what is the distance from P to Q? |
A) 14 km
B) 8 km
C) 12 km
D) 6 km
Correct Answer: C
Solution :
| Distance between P and Q |
| \[=\frac{T\,({{x}^{2}}-{{y}^{2}})}{2x}=\frac{3\,({{9}^{2}}-{{3}^{2}})}{2\times 9}\] [here, \[x=9,\] \[y=3\] and \[T=3\]] |
| \[=\frac{3\times (81-9)}{18}=\frac{3\times 72}{18}=12\,\,km\] |
| Alternate Method |
| Speed of stream \[=3\,\,km/h\] |
| Speed of boat in still water \[=9\,\,km/h\] |
| \[\therefore \]Speed in upstream \[=9-3=6\,\,km/h\] |
| Speed in downstream \[=9+3=12\,\,km/h\] |
| According to the question, |
| \[\frac{x}{6}+\frac{x}{12}=3\]\[\Rightarrow \]\[\frac{2x+x}{12}=3\] |
| \[\Rightarrow \] \[3x=36\]\[\Rightarrow \]\[x=12\,\,km\] |
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