speed of a boat in still water is 15 km per hour and speed of a stream is 5 kilometre per hour find the time taken by the boat to cover 40 kilometre upstream and 36 km downstream
Answers
Answer:
Given :
Speed of boat in still water = 15 \ km/hr=15 km/hr
Let xx be speed of the stream in {km}/{hr}km/hr
Speed of the boat upstream =15-x=15−x
Speed of the boat down stream = 15+x=15+x
Time taken for upstream { T }_{ 1 }=\dfrac { 30 }{ 15-x }T
1
=
15−x
30
Time taken for downstream { T }_{ 2 }=\dfrac { 30 }{ 15+x }T
2
=
15+x
30
Given, { T }_{ 1 }+{ T }_{ 2 }=\dfrac { 9 }{ 2 }T
1
+T
2
=
2
9
=\dfrac { 30 }{ 15-x } +\dfrac { 30 }{ 15+x } =\dfrac { 9 }{ 2 }=
15−x
30
+
15+x
30
=
2
9
=30\left( \dfrac { 1 }{ 15-x } +\dfrac { 1 }{ 15+x } \right) =\dfrac { 9 }{ 2 }=30(
15−x
1
+
15+x
1
)=
2
9
=30\left( \dfrac { 15+x\div 15-x }{ \left( 15-x \right) \left( 15+x \right) } \right) =\dfrac { 9 }{ 2 }=30(
(15−x)(15+x)
15+x÷15−x
)=
2
9
=\dfrac { 30\times 30 }{ 225-{ x }^{ 2 } } =\dfrac { 9 }{ 2 }=
225−x
2
30×30
=
2
9
=\dfrac { 100 }{ 225-{ x }^{ 2 } } =\dfrac { 1 }{ 2 }=
225−x
2
100
=
2
1
\Rightarrow 225-{ x }^{ 2 }=200⇒225−x
2
=200
\Rightarrow { x }^{ 2 }=25⇒x
2
=25
\Rightarrow x=5⇒x=5 ....(\because x∵x is +ve)
\Rightarrow x=5 \ km/hr⇒x=5 km/hr
Speed of the stream =5 \ km/hr=5 km/hr.
Answer:
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