To determine the equation that represents the total meters \( m \) that Sam runs in \( t \) minutes, we first need to understand how much Jacob runs.
Let's analyze the information given about Sam:
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Let \( J(t) \) be the distance Jacob runs in \( t \) minutes. The graph should provide the equation for Jacob's running, which is typically in the form \( m = rt \), where \( r \) is the rate (in meters per minute).
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If Sam runs 15 meters less each minute than Jacob, we can express Sam's running rate as: \[ S(t) = J(t) - 15 \] where \( J(t) \) is Jacob's distance formula.
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Based on the options you provided, it seems that we need to consider potential rates for Jacob and then determine Sam's.
Let’s consider the possible equations provided:
- \( m = 200t \)
- \( m = 185t \)
- \( m = 215t \)
- \( m = 15t \)
If we assume Jacob runs at a certain rate and then subtract 15 from it for Sam's running rate:
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If \( m = 200t \), then Sam's rate would be \( 200 - 15 = 185 \), giving \( m = 185t \).
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If \( m = 185t \), then Sam's rate would be \( 185 - 15 = 170 \) (not in the given options).
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If \( m = 215t \), then Sam's rate would be \( 215 - 15 = 200 \) (not in the given options).
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If \( m = 15t \), then Sam's rate would be \( 15 - 15 = 0 \) (not plausible).
Based on the logical deductions, if Jacob runs \( 200t \), then Sam runs \( 185t \).
Thus, the equation that represents the total meters \( m \) that Sam runs in \( t \) minutes is:
\[ m = 185t \]
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