A boat takes one-third the time travelling the same distance when it goes downstream than upstream. What is the ratio of the speed in still water to the speed of the current?

A boat takes one-third the time travelling the same distance when it goes downstream than upstream. What is the ratio of the speed in still water to the speed of the current?
1). 3 : 1
2). 2 : 1
3). 1 : 2
4). 1 : 3

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Guest · Answer 1 · 2019-07-08 23:04:06

Let the distance travelled be x km

Let the speed of current be v km/hr

Let the speed of boat in still water be b km/hr

∴ Speed of boat upstream = (b – v) km/hr

⇒ Speed of boat downstream = (b + v) km/hr

∴ Time taken to travel x distance upstream = x/(b – v) hr

⇒ Time taken to travel x distance downstream = x/(b + v) hr

Now, $(\frac{{{\rm{x}}/\left( {{\rm{b\;}}-{\rm{\;v}}} \right){\rm{\;}}}}{{{\rm{x}}/\left( {{\rm{b\;}} + {\rm{\;v}}} \right){\rm{\;}}}})$ = 3

⇒ b + v = 3(b – v)

⇒ b + v = 3b – 3v

⇒ 4v = 2b

⇒ b/v = 2 : 1

∴ Ratio of speed in still water to speed of current is 2 : 1

A boat takes one-third the time travelling the same distance when it goes downstream than upstream. What is the ratio of the speed in still water to the speed of the current?

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