| 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) 4.5 km/h
B) 5.2 km/h
C) 2.5 km/h
D) 3 km/h
Correct Answer: D
Solution :
| Let the speed of the boat in still water be \[x\,\,km/h.\] |
| \[\therefore \]The speed of the boat along the current\[=(x+1)\,\,km/h\] |
| and the speed of the boat against the current |
| \[=(x-1)\,\,km/h\] |
| \[\therefore \] \[\frac{4}{x+1}+\frac{4}{x-1}=3\] |
| \[\Rightarrow \]\[\frac{4\,(x+1+x-1)}{(x+1)(x-1)}=3\] |
| \[\Rightarrow \] \[8x=3{{x}^{2}}-3\] |
| \[\Rightarrow \] \[3{{x}^{2}}-8x-3=0\] |
| \[\Rightarrow \]\[3{{x}^{2}}-9x+x-3=0\] |
| \[\Rightarrow \]\[(x-3)(3x+1)=0\] |
| \[\therefore \] \[x=3,\]\[-\frac{1}{3}\] |
| Hence, speed of boat in still water is \[3\,\,km/h.\] |
You need to login to perform this action.
You will be redirected in
3 sec
