Maths Olympiad Prep

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Algebra Difficulty 2.1 Junior Find the answer

After school, Maya and Naomi headed to the beach, 66 miles away. Maya decided to bike while Naomi took a bus. The graph below shows their journeys, indicating the time and distance traveled. What was the difference, in miles per hour, between Naomi's and Maya's average speeds?

Pick one

Solution

Naomi travels 66 miles in a time of 1010 minutes, which is equivalent to 16\dfrac{1}{6} of an hour. Since speed=distancetime\text{speed} = \frac{\text{distance}}{\text{time}}, her speed is 6(16)=36\frac{6}{\left(\frac{1}{6}\right)} = 36 mph. By a similar calculation, Maya's speed is 1212 mph, so the answer is 36−12=(E) 2436-12 = \boxed{\textbf{(E) }24}.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.