A boat covers a certain distance downstream in \(\frac{1}{2}\) hour,

1.	A boat covers a certain distance downstream in \(\frac{1}{2}\) hour, while it comes back in \(1\frac{1}{2}\) hours. If the speed of the stream be 5 kmph. What is the speed of the boat in still water?1. 10 kmph2. 12 kmph3. 13 kmph4. 15 kmph
Answer» Correct Answer - Option 1 : 10 kmph Given: A boat covers a certain distance downstream in 1/2 hour, while it comes back in 3/2 hours. The speed of the stream is 5 km/hr. Concept used: Speed = \(\frac{{Distan ce}}{{Time}}\) Calculation: Let the speed of the boat be x km/hr Let the speed of the current be y km/hr Speed of the Boat downstream = (x + y) km/hr Speed of the Boat upstream = (x - y) km/hr x + y = \(\frac{D}{{\frac{1}{2}}}\) x + y = 2D - (i) x - y = \(\frac{D}{{\frac{3}{2}}}\) x - y = \(\frac{{2D}}{3}\) - (ii) As per the Question, Speed of the stream is 5 km/hr. Now using equation i and ii \(\frac{{x + 5}}{{x - 5}} = 3\) x + 5 = 3x - 15 2x = 20 x = 10 km/hr

A boat covers a certain distance downstream in \(\frac{1}{2}\) hour, while it comes back in \(1\frac{1}{2}\) hours. If the speed of the stream be 5 kmph. What is the speed of the boat in still water?1. 10 kmph2. 12 kmph3. 13 kmph4. 15 kmph

Answer» Correct Answer - Option 1 : 10 kmph

Given:

A boat covers a certain distance downstream in 1/2 hour, while it comes back in 3/2 hours.

The speed of the stream is 5 km/hr.

Concept used:

Speed = \(\frac{{Distan ce}}{{Time}}\)

Calculation:

Let the speed of the boat be x km/hr

Let the speed of the current be y km/hr

Speed of the Boat downstream = (x + y) km/hr

Speed of the Boat upstream = (x - y) km/hr

x + y = \(\frac{D}{{\frac{1}{2}}}\)

x + y = 2D - (i)

x - y = \(\frac{D}{{\frac{3}{2}}}\)

x - y = \(\frac{{2D}}{3}\) - (ii)

As per the Question,

Speed of the stream is 5 km/hr.

Now using equation i and ii

\(\frac{{x + 5}}{{x - 5}} = 3\)

x + 5 = 3x - 15

2x = 20

x = 10 km/hr

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