| A boat travels upstream from Q to P and downstream from P to Q in 3 h. If the distance between P to Q is 4 km and the speed of the current is 1 km/h, then what is the speed of the boat in still water? |
A) 1.5 km/h
B) 5.2 km/h
C) 4.5 km/h
D) 3 km/h
Correct Answer: D
Solution :
| Let speed of boat in still water \[=x\,\,km/h\] |
| Upstream \[=\frac{4}{x-1}\]and downstream \[=\frac{4}{x+1}\] |
| So, \[\frac{4}{x-1}+\frac{4}{x+1}=3\]\[\Rightarrow \]\[\frac{4\,(x+1)+4\,(x-1)}{{{x}^{2}}-1}=3\] |
| \[\Rightarrow \]\[\frac{4x+4+4x-4}{{{x}^{2}}-1}=3\]\[\Rightarrow \]\[8x=3{{x}^{2}}-3\] |
| \[\Rightarrow \] \[3{{x}^{2}}-8x-3=0\] |
| \[\Rightarrow \] \[3{{x}^{2}}-9x+x-3=0\] |
| \[\Rightarrow \]\[3x\,\,(x-3)+1\,\,(3x+1)=0\] |
| \[\Rightarrow \] \[(x-3)(3x+1)=0\] |
| \[\therefore \] \[x=3km/h\] |
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