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bkraabel
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Homework Statement
Runners A, B, and C run a 100-m race, each at a constant speed.
Runner A takes first place, beating runner B by 10 m. Runner
B takes second place, beating runner C by 10 m. By what time
interval does runner A beat runner C?
Homework Equations
d = 100 m
Δd = 10 m
Δt[itex]_{i}[/itex] = time for runner i to travel 100 m
v[itex]_{i}[/itex] = speed of runner i
The Attempt at a Solution
Can this problem be solved without knowing the speed of one of the runners? Here's a few equalities for this problem:
v[itex]_{a}[/itex] = [itex]\frac{d}{Δt_{a}}[/itex]
v[itex]_{b}[/itex] = [itex]\frac{d-Δd}{Δt_{a}}[/itex]
v[itex]_{c}[/itex] = [itex]\frac{v_{b}Δt_{b}-Δd}{Δt_{b}}[/itex]