Question

chloe and owen are participating in a hiking challenge to reach a peak at 15 miles away from base camp. a graph representing their progress during the first hour is shown in the standard (x,y) coordinate plane provided. assume that chloe continues to travel at the same speed until she reaches the peak. by how much will owen need to increase his average speed for the remainder of the challenge in order to reach the peak at exactly the same time as chloe?

Explanation:

Step1: Calculate Chloe's speed

Chloe's speed: $v_{Chloe} = \frac{3\ \text{miles}}{1\ \text{hour}} = 3\ \text{mph}$

Step2: Find Chloe's total time

Total time for Chloe: $t_{total} = \frac{15\ \text{miles}}{3\ \text{mph}} = 5\ \text{hours}$

Step3: Calculate Owen's first hour distance

Owen's first hour distance: ~1 mile (from graph)

Step4: Find Owen's remaining time

Remaining time for Owen: $5 - 1 = 4\ \text{hours}$

Step5: Find Owen's remaining distance

Remaining distance for Owen: $15 - 1 = 14\ \text{miles}$

Step6: Calculate Owen's required speed

Required speed: $v_{required} = \frac{14}{4} = 3.5\ \text{mph}$

Step7: Find speed increase

Increase: $3.5 - 1 = 2.5\ \text{mph}$

Answer:

2.5 mph