An aeroplane travels 1000 km with tailwind in same time that it travels
600 km against a headwind. If the speed of aeroplane is 500 km/h in still
air, what is the speed of wind?
Answers
125 km/h is the speed of wind
Step-by-step explanation:
GIVEN
Aeroplane travels with tailwind = 1000 km
Aeroplane travels against headwind = 600 km
Speed of aeroplane in still wind = 500 km/h
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TO FIND
Speed of wind
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Let's take speed of wind as x
___________________________
We know that,
Speed with tailwind = ( 500 + x ) km/h
Speed against headwind = ( 500 - x ) km/h
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We know that,
Time = Distance / Speed
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Therefore
Time with tailwind
= 1000 / ( 500 + x ) ..... ( equation 1 )
Time against headwind
= 600 / ( 500 - x ) ..... ( equation 2 )
___________________________
We know that,
An aeroplane travels 1000 km with tailwind in same time that it travels that is 600 km against a headwind
Therefore,
1000 / ( 500 + x ) = 600 / ( 500 - x )
= 10 / ( 500 + x ) = 6 / ( 500 - x )
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Now
To get the value of x
We need to cross multiply equation 1 and equation 2
Therefore,
10 / ( 500 + x ) = 6 / ( 500 - x )
5000 - 10x = 3000 - 6x
5000 - 3000 = 10 + 6x
5000 - 3000 = 16x
2000 = 16x
x = 2000 / 16
x = 125