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:
`(1)/(7)`

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)=(distance)/(time\ taken)`

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

`2.8=(x+y)/(\frac){x}{2}+(y)/(3)}`

Let
`(x)/(y)=z`

`2.8=(z+1)/((z)/(2)+(1)/(3))`

`z=(1)/(6)`

Fraction of distance traveled on sunny weather

`(x)/(x+y)=(z)/(z+1)=(1)/(7)`