While traveling on a highway, Hermione and Draco passed checkpoint R at 8 am and 9 am, moving at speeds of 35 mph and 45 mph respectively. Professor McGonagall began cycling in the same direction from point S at 7 am at 20 mph. If Hermione and Draco met each other at S, what distance from S did Draco meet Professor?

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130

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150

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Given: • While traveling on a highway, Hermione and Draco passed checkpoint R at 8 am and 9 am, moving at speeds of 35 mph and 45 mph respectively. • Professor McGonagall began cycling in the same direction from point S at 7 am at a speed of 20 mph. • Hermione and Draco met each other at S. To find: • The distance from S, where Draco met Professor McGonagall. Approach and Working: Since Hermione and Draco passed checkpoint R at 8 am and 9 am, we can determine that • At 9 am, the distance between Hermione and Draco = distance covered by Hermione in 1 hour = 35 miles. Now, with Hermione's and Draco's speeds being 35 mph and 45 mph respectively, we find that • From 9 am, Draco met Hermione in

\frac{35}{45 - 35}

hours, or in 3.5…

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What this question tests

What it tests

Your application of distance = rate × time to trains, boats, and commuters, including relative speed.

Common trap

Mixing units (miles per hour vs. minutes) or averaging speeds — average speed is total distance over total time.