Asked by D4VD
Describing the Effect of Rate of Change
Amy is biking to school from her father's house and Jeremy is biking to school from his aunt's house. Suppose Amy is moving at a rate 10 miles per hour and Jeremy is moving at a rate of 8 miles per hour. Can you assume that Amy will get to school first? Explain.
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You cannot assume Amy will get there first just because she rides faster. Arrival time depends on distance (and start times), since time = distance / speed.
If they start at the same time and maintain constant speeds, Amy arrives before Jeremy exactly when
d_A/10 < d_J/8,
i.e. when d_A < 1.25·d_J. So Amy will get there first only if her distance to school is less than 1.25 times Jeremy’s distance.
Counterexample: if Amy is 20 miles away and Jeremy 10 miles away, Amy’s time = 20/10 = 2 hours, Jeremy’s time = 10/8 = 1.25 hours, so Jeremy arrives first despite being slower. Conversely, if they live the same distance from school, Amy (faster) would arrive first.
If they start at the same time and maintain constant speeds, Amy arrives before Jeremy exactly when
d_A/10 < d_J/8,
i.e. when d_A < 1.25·d_J. So Amy will get there first only if her distance to school is less than 1.25 times Jeremy’s distance.
Counterexample: if Amy is 20 miles away and Jeremy 10 miles away, Amy’s time = 20/10 = 2 hours, Jeremy’s time = 10/8 = 1.25 hours, so Jeremy arrives first despite being slower. Conversely, if they live the same distance from school, Amy (faster) would arrive first.
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