Question

If a boat takes 4 h longer to travel a distance of
45 km upstream than to travel the same distance
downstream, then find the speed of the boat in still
water if the speed of the stream is 2 km/h.​

Answer 1

Answer :

The speed of the boat in still water is 7km/h

Given :

• The distance travelled by the boat both upstream and downstream is 45km
• It takes 4h longer to travel the same distance upstream than downstream.
• The speed of stream is 2km/h

To Find :

• The speed of the boat in still water.

Solution :

Let us consider the speed of boat be x km/hr and the speed of stream be y km/h

The speed at downstream is (x + y)km/h

and at upstream is (x - y)km/h

$\sf{We \: \: know \: \: that }$

$\sf{speed = \dfrac{distance}{time}}$

$\sf{time=\dfrac{distance}{speed}}$

We are given that time taken at upstream is 4hr longer than downstream , therefore ,

$\sf{\implies \dfrac{45}{x - y} - \dfrac{45}{x + y}= 4}\\\\ \sf{\implies\dfrac{45(x + y) -45(x - y)}{(x -y)(x + y)}= 4}\\\\ \sf{\implies 45(x + y - x + y) = 4(x - y)(x + y)}\\\\ \sf{\implies 45\times2y = 4(x^{2} - y^{2} )}\\\\ \sf{\implies 90y = 4(x^{2} - y^{2})}\\\\ \sf{\implies 90\times2 = 4(x^{2} - 2^{2} )} \{since \: \: the \: \:speed \: \: of \: \: stream \: \: is \: 2km/h\} \\\\ \sf{\implies 180 = 4(x^{2} - 4) }\\\\ \sf{\implies 180 = 4x^{2} - 16}\\\\ \sf{\implies 4x^{2} = 180 + 16}\\\\ \sf{\implies x^{2} = \dfrac{196}{4}}\\\\ \sf{\implies x^{2} = 49}\\\\ \sf{\implies x^{2} = 7^{2} }\\\\ \implies\bf{x = \pm7km/h}$

Therefore either

⇒x = 7 or ⇒x = -7

Since , speed can never be negative so x ≠ -7

Thus , speed of the in still water is 7km/h

Answer 2

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QUESTION -

If a boat takes 4 h longer to travel a distance of 45 km upstream than to travel the same distance downstream, then find the speed of the boat in still water if the speed of the stream is 2 km/h.

SOLUTION -

In the above Question, we have the following information given ....

A boat takes 4 h longer to travel a distance of 45 km upstream than to travel the same distance downstream.

the speed of the stream is 2 km/h.

Let us assume the speed of the the boat in still water to be B kmph.

So,

Speed Upstream = ( B - 2 ) kmph

Speed Downstream = ( B + 2 ) kmph.

Now,

The net distance is 45 km.

We can thus frame the following Equation -

=> $\dfrac{ 45 } { B - 2 } + \dfrac{ 45 } { B + 2 } = 4$

.

.

.

.

Solving , Finally we get that : B = 7 kmph.

So, the required speed of the boat is 7 kmph.

=> It's speed Upstream is ( 7 - 2 ) kmph = 5 kmph.

=> It's speed Downstream is ( 7 + 2 ) kmph = 9 kmph.

ANSWER :

The required speed of the boat in still water is 7 kmph.