Question

At the beginning of my bike ride I feel good, so I can travel 20 miles per hour. Later, I get tired and travel only 12 miles per hour. If I travel a total of 122 miles in a total time of 8 hours, for how many hours did I feel good? Express your answer as a common fraction.

Answer 1

Answer: $3\dfrac{1}{4}$ hours

Step-by-step explanation:

Let x be the time ( in hours ) you feel good and y be the time ( in hours ) that you get tired.

As per given , we have

x+y= 8

Since : $Distance = Speed\times Time$

So , we have

20x+12y=122

According to the given question , we have the following system of equations ,

$x+y= 8--------(1)\\\\20x+12y=122------------------(2)$

Multiply 12 on both sides of equation (1) , we get

$12x+12y=96------------(3)$

Eliminate equation (3) from (2) , we get

$8x=26\\\\\Rightarrow\ x=\dfrac{13}{4}=3\dfrac{1}{4}$

Hence, you felt $3\dfrac{1}{4}$ hours good.