Respuesta :
So, we know that it takes Sam 1 mph up and 9 mph down and it takes Liam both 2 mph down and up the hill. So if we divide the 2 mph for Liam by 2 miles (the whole length of the hill) we will get 1 or 1 hour. Then we do 1/1 (i don't know how to explain this part of why we do that, sorry) and than we do 1 / 9 and we get 1/9 so we add them and get 1 1/9 so that's Sam's time.
So, Liam took one hour and Sam took 1 and 1/9 hours, in conclusion liam was faster
(I'm really sorry for my bad explaining, i tried my best)
Sam took [tex]1\frac{1}{9}[/tex] hours and Liam took 1 hour to finish. Liam was the winner.
Given in the question,
- Sam's average speed up the hill is 1 mph and average speed down the hill is 9 mph.
- Liam ran up the hill and down the hill with the same speed 2 mph.
- Length of the path from bottom to top of the hill is 1 mile.
By using the expression for the speed,
[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]
[tex]\text{Time}=\frac{\text{Distance}}{\text{Speed}}[/tex]
For Sam,
Time taken in going up the hill = [tex]\frac{1}{1}[/tex]
= 1 hour
Time taken in going down the hill = [tex]\frac{1}{9}[/tex] hours
Therefore, total time taken by Sam in going up and down the hill = [tex]1\frac{1}{9}[/tex] hours
For Liam,
Time taken in going up the hill = [tex]\frac{1}{2}[/tex] hours
Time taken in going down the hill = [tex]\frac{1}{2}[/tex] hours
Total time taken in going up and down the hill = [tex]\frac{1}{2}+\frac{1}{2}[/tex]
= 1 hour
Therefore, Sam took [tex]\frac{1}{9}[/tex] hours more than Liam.
Hence, Liam was the winner.
Learn more,
https://brainly.com/question/10367940
