The rate of plane is 657 kmph and rate of wind is 65 kmph.
Step-by-step explanation:
Given,
Distance covered against wind in 3 hours = 1776 kilometers
Distance covered with the wind in 3 hours = 2166 kilometers
We know that;
Distance = Speed*Time
Speed = Distance/Time
Let,
x be the speed of plane and y be the speed of wind.
Speed while travelling against the wind;
[tex]x-y=\frac{1776}{3}\\x-y=592\ \ \ Eqn\ 1[/tex]
Speed while travelling with the wind
[tex]x+y=\frac{2166}{3}\\x+y=722\ \ \ Eqn\ 2[/tex]
Adding Eqn 1 and 2
[tex](x-y)+(x+y)=592+722\\x-y+x+y=1314\\2x=1314[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{1314}{2}\\x=657[/tex]
Putting x=657 in Eqn 2
[tex]657+y=722\\y=722-657\\y=65[/tex]
The rate of plane is 657 kmph and rate of wind is 65 kmph.
Keywords: distance, speed
Learn more about speed at:
- brainly.com/question/4168505
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