| A boat can travel 4.2 km upstream in 14 min. If the respective ratio of speed of the boat in still water and speed of the stream is 7: 1. How much time will the boat take to cover 17.6 km downstream? |
A) 52 min
B) 44 min
C) 48 min
D) 36 min
E) 54 min
Correct Answer: B
Solution :
| Let the speed of boat in still water be 7x km/h and speed of stream be x km/h. |
| \[\therefore \] Speed in upstream \[=7x-x=6x\,km/h\] |
| \[\therefore \] \[6x=\frac{4.2\,km}{14\,\min }\] |
| \[\Rightarrow \] \[6x=\frac{4.2}{14}\times 60\,km/h\] |
| \[\Rightarrow \] \[x=\frac{42\times 60}{10\times 14\times 6}\]\[\Rightarrow \]\[x=3\] |
| Speed of boat in still water \[=7\times 3=21\,km/h\] |
| Speed of stream = 3 km/h |
| Distance downstream = 17.6 km |
| Speed in downstream \[=21+3=24\,km/h\] |
| \[\text{Time}=\frac{\text{Distance}}{\text{Speed}}=\frac{17.6}{24}h\] |
| \[=\frac{17.6}{24}\times 60\min =44\min \] |
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