A boat takes one-third the time travelling the same distance when it g

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?1). 3 : 12). 2 : 13). 1 : 24). 1 : 3
Answer» 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?1). 3 : 12). 2 : 13). 1 : 24). 1 : 3

Answer»

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

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