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On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction of the total distance did he cover while the sun was shining on him?

Respuesta :

Answer:[tex]\frac{1}{7}[/tex]

Step-by-step explanation:

Given

sunny day speed= s mph

Rainy day speed=s+1 mph

Derek average speed =2.8 miles/hr

s<2.8<s+1

so on sunny day speed must be 2 mph

and on rainy day speed must be 3 mph

[tex]v_{avg}=\frac{distance}{time\ taken}[/tex]

Let x be the distance traveled in sunny and y be the distance traveled in rainy weather

[tex]2.8=\frac{x+y}{\frac}{x}{2}+\frac{y}{3}}[/tex]

Let [tex]\frac{x}{y}=z[/tex]

[tex]2.8=\frac{z+1}{\frac{z}{2}+\frac{1}{3}}[/tex]

[tex]z=\frac{1}{6}[/tex]

Fraction of distance traveled on sunny weather

[tex]\frac{x}{x+y}=\frac{z}{z+1}=\frac{1}{7}[/tex]

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