Answer:
Part A. At least 6 hours
Part B. In less than 2.5 hours Elijah will be behind Mercedes
Part C. In more than 2.5 hours Elijah will be ahead Aubrey
Step-by-step explanation:
D = distance
v =speed
t = time
Formula connecting D, v and t:
![D=v\cdot t](https://tex.z-dn.net/?f=D%3Dv%5Ccdot%20t)
Part A.
Steve's speed: ![v=3.5\ mph](https://tex.z-dn.net/?f=v%3D3.5%5C%20mph)
Distance: at least 21 miles
Time: unknown, so
![3.5\cdot t\ge 21\\ \\35t\ge 210\ [\text{Multiplied by 10}]\\ \\t\ge \dfrac{210}{35}\\ \\t\ge \dfrac{30}{5}\\ \\t\ge 6](https://tex.z-dn.net/?f=3.5%5Ccdot%20t%5Cge%2021%5C%5C%20%5C%5C35t%5Cge%20210%5C%20%5B%5Ctext%7BMultiplied%20by%2010%7D%5D%5C%5C%20%5C%5Ct%5Cge%20%5Cdfrac%7B210%7D%7B35%7D%5C%5C%20%5C%5Ct%5Cge%20%5Cdfrac%7B30%7D%7B5%7D%5C%5C%20%5C%5Ct%5Cge%206)
It would take Steve at least 6 hours to walk at least 21 mi on Day 1.
Part B.
Mercedes's speed: ![v_M=2.4\ mph](https://tex.z-dn.net/?f=v_M%3D2.4%5C%20mph)
Elijan's speed: ![v_E=3.2\ mph](https://tex.z-dn.net/?f=v_E%3D3.2%5C%20mph)
Elijan's Distance walked:
miles
Mercedes's Distance walked:
miles
Time: x hours
Mercedes is 2 miles ahead, so
![D_E=3.2x\\ \\D_M=2.4x+2](https://tex.z-dn.net/?f=D_E%3D3.2x%5C%5C%20%5C%5CD_M%3D2.4x%2B2)
Elijan will be behind when
![D_E](https://tex.z-dn.net/?f=D_E%3CD_M%5C%5C%20%5C%5C3.2x%3C%202.4x%2B2%5C%5C%20%5C%5C3.2x-2.4x%3C2%5C%5C%20%5C%5C0.8x%3C2%5C%5C%20%5C%5C8x%3C20%5C%20%5B%5Ctext%7BMultiplied%20by%2010%7D%5D%5C%5C%20%5C%5Cx%3C%5Cdfrac%7B20%7D%7B8%7D%5C%5C%20%5C%5Cx%3C2.5%5C%20hours)
In 2.5 hours Elijan will catch up Mercedes, and in less than 2.5 hours Elijah will be behind Mercedes.
Part C.
Aubrey's speed: ![v_M=3\ mph](https://tex.z-dn.net/?f=v_M%3D3%5C%20mph)
Elijan's speed: ![v_E=3.2\ mph](https://tex.z-dn.net/?f=v_E%3D3.2%5C%20mph)
Elijan's Distance walked:
miles
Aubrey's Distance walked:
miles
Time: x hours
At the beginning of Day 3, Elijah starts walking at the marker for Mile 42, and Aubrey starts walking at the marker for Mile 42.5.
![D_E=42+3.2x\\ \\D_A=42.5+3x](https://tex.z-dn.net/?f=D_E%3D42%2B3.2x%5C%5C%20%5C%5CD_A%3D42.5%2B3x)
Elijan will be ahead of Aubrey when
![D_E>D_A\\ \\42+3.2x> 42.5+3x\\ \\3.2x-3x>42.5-42\\ \\0.2x>0.5\\ \\2x>5\ [\text{Multiplied by 10}]\\ \\x>\dfrac{5}{2}\\ \\x>2.5\ hours](https://tex.z-dn.net/?f=D_E%3ED_A%5C%5C%20%5C%5C42%2B3.2x%3E%2042.5%2B3x%5C%5C%20%5C%5C3.2x-3x%3E42.5-42%5C%5C%20%5C%5C0.2x%3E0.5%5C%5C%20%5C%5C2x%3E5%5C%20%5B%5Ctext%7BMultiplied%20by%2010%7D%5D%5C%5C%20%5C%5Cx%3E%5Cdfrac%7B5%7D%7B2%7D%5C%5C%20%5C%5Cx%3E2.5%5C%20hours)
In 2.5 hours Elijan will catch up Aubrey, and in more than 2.5 hours Elijah will be ahead Aubrey.