| A boat takes 19 h for travelling downstream from point A to point B and coming back to a point C mid-way between A and B. If the velocity of the stream is 4 km/h and the speed of the boat in still water is 14 km/h, what is the distance between A and B? |
A) 160 km
B) 180 km
C) 200 km
D) 220 km
Correct Answer: B
Solution :
| Speed downstream |
| \[=(14+4)\,km/h=18\,km/h\] |
| Speed upstream \[=(14-4)\,km/h=10\,km/h\] |
| Let the distance between A and B be x km. |
| Then, \[\frac{x}{18}+\frac{(x/2)}{10}=19\] |
| \[\Rightarrow \] \[\frac{x}{18}+\frac{x}{20}=19\] |
| \[\Rightarrow \] \[\frac{19x}{180}=19\] |
| \[\Rightarrow \] \[x=180\,km\] |
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