Answer:
a. i. 1.11 h ii. 1 h. b. Liam
Step-by-step explanation:
a.
i. Sam's time
We know distance d = vt where v = speed and t = time.
Since our distance here is the length of the path, d = 1 mile.
For Sam, his speed up the hill is v = 1 mph, so, the time it takes him to go uphill is t = d/v = 1 mi/1 mph = 1 h.
He goes down hill at a speed of v = 9 mph, so the time it takes him to go down hill is t = d/v = 1 mi/9 mph = 1/9 h = 0.11 h
So, the total time it takes him to complete the trip is t = 1 h + 0.11 h = 1.11 h
ii. Liam's time
For Liam, his speed both uphill and downhill is v = 2 mph, so, the time it takes to cover each trip is t = d/v = 1 mi/2 mph = 0.5 h.
So for both uphill and downhill trip, the total time is t' = 2 × 0.5 h = 1 h
b. Since Liam's time t' = 1 h < Sam's time t = 1.11 h, that is t' = 1h < t = 1.11 h, Liam is the winner.
