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# Writing expressions and equations

During a marathon, Kim our champion cyclist is having struggles. At the halfway checkpoint she is behind the leader, Allison by 10 miles. Kim still has a lot of energy left and pacing herself at a constant 15 miles per hour. Allison on the other hand, is getting tired and has slowed down to 11 miles per hour.

a) Write an expression that relates Kim's distance beyond the checkpoint and the number of hours that have elapsed since she passed the checkpoint
b) Write an expression that relates Allison's distance beyond the checkpoint and the number of hours since Kim passed the checkpoint
c) Write and solve an equation that represents when Allison will finish the marathon if it's 50 miles.
d) Write and solve an equation that represents when Kim will finish the marathon if it's 50 miles

#### Solution Preview

a) If we let x(t) be Kim's distance in miles beyond the checkpoint and t be the number of hours that have elapsed since she passed the checkpoint, then we have

x(t) = 15 t.

b) If we let y be Allison's distance in miles beyond the checkpoint, then we ...

#### Solution Summary

We solve some algebra problems pertaining to a marathon race.

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