The rate of wind was 5 kilometer per hour.
Step-by-step explanation:
Given,
Time taken for riding against the wind = 1 hour
Distance traveled = 15 km
Speed = [tex]\frac{Distance}{Time}[/tex]
Combined Speed = [tex]\frac{15}{1}=15\ km/h[/tex]
Time taken for riding with the wind = 36 minutes = [tex]\frac{36}{60}=\frac{3}{5}\ hour[/tex]
Speed = [tex]\frac{Distance}{Time}[/tex]
Speed = [tex]\frac{15}{\frac{3}{5}}=\frac{15*5}{3}=25\ km/h[/tex]
Let,
x represent the rate of bike.
y represent the rate of wind.
When the bike goes against, we will subtract the speed of wind from speed of bike.
x-y=15 Eqn 1
x+y=25 Eqn 2
Adding Eqn 1 and 2
[tex](x-y)+(x+y)=15+25\\x-y+x+y=40\\2x=40[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{40}{2}\\x=20[/tex]
Putting x=20 in Eqn 2
[tex]20+y=25\\y=25-20\\y=5[/tex]
The rate of wind was 5 kilometer per hour.
Keywords: linear equation, speed
Learn more about speed at:
#LearnwithBrainly
