Bob takes the subway to work and uses an escalator at the railway station. If Bob runs up 8 steps of the escalator, then it takes him 46.5 seconds to reach the top of the escalator. If he runs up 13 steps of the escalator, then it takes him only 39.0 seconds to reach the top. How many seconds would it take Bob to reach the top if he did not run up any steps of the escalator?

x – 8y = 46.5

x – 13y = 39.0

subtract the equations to solve for y

5 y = 46.5 – 39

y = 1.5 so he saves 1.5 seconds per step he runs.

sub in y to solve for x

x – 8 (1.5) = 46.5

x – 12 = 46.5

x = 58.5 seconds

We could have solved for x directly, but the computation is messy.

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