Question

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?

Answer 1

Answer:$\frac{1}{7}$

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

$v_{avg}=\frac{distance}{time\ taken}$

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

$2.8=\frac{x+y}{\frac}{x}{2}+\frac{y}{3}}$

Let $\frac{x}{y}=z$

$2.8=\frac{z+1}{\frac{z}{2}+\frac{1}{3}}$

$z=\frac{1}{6}$

Fraction of distance traveled on sunny weather

$\frac{x}{x+y}=\frac{z}{z+1}=\frac{1}{7}$