Staircase Encounter
Algebra
Level
2
David runs up the stairs from the 11th floor at 57 floors per minute. Albert runs down the stairs from the 51st floor at 63 floors per minute. If they start at the same time, on which floor will they meet?
28
37
30
19
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1 solution
We can model the floor that David is on by the function D ( t ) = 1 1 + 5 7 t where t is time in minutes since he started. Similarly, Albert's floor can be modeled by A ( t ) = 5 1 − 6 3 t .
Since we're interested in where these paths cross, we'll set these equations equal to each other, giving us 1 1 + 5 7 t = 5 1 − 6 3 t ⟶ t = 3 1 . Plugging t = 3 1 in each function returns 30, telling us they meet on the 30th floor.