Question

Sam and Liam raced each other up and then down the hill. Sam's average speed up the hill was 1 mph, and his average speed down the hill was 9 mph. Liam ran up the hill and down the hill with the same speed, 2 mph. If the path from the bottom to the top of the hill is 1 mile long, how much time did it take each of the boys to finish - and who was the winner?

Answer 1

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)