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.
Answers
Step-by-step explanation:
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 }Weknowthat
\sf{speed = \dfrac{distance}{time}}speed=
time
distance
\sf{time=\dfrac{distance}{speed}}time=
speed
distance
We are given that time taken at upstream is 4hr longer than downstream , therefore ,
\begin{lgathered}\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}\end{lgathered}
⟹
x−y
45
−
x+y
45
=4
⟹
(x−y)(x+y)
45(x+y)−45(x−y)
=4
⟹45(x+y−x+y)=4(x−y)(x+y)
⟹45×2y=4(x
2
−y
2
)
⟹90y=4(x
2
−y
2
)
⟹90×2=4(x
2
−2
2
){sincethespeedofstreamis2km/h}
⟹180=4(x
2
−4)
⟹180=4x
2
−16
⟹4x
2
=180+16
⟹x
2
=
4
196
⟹x
2
=49
⟹x
2
=7
2
⟹x=±7km/h
Step-by-step explanation:
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