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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]