Final answer:
To find the distance Megan cycles, we first determined Rhodri's travel time and then calculated Megan's travel time by subtracting 5 minutes. Using Megan's average speed and her travel time, we found out that Megan cycles 2 miles to the swimming pool.
Step-by-step explanation:
To solve the mathematical problem completely, we need to calculate the distance Megan cycles, given that Rhodri's journey by car is 5.5 miles with an average speed of 22 mph, and Megan's average speed on her bike is 12 mph. Megan arrives at the swimming pool 5 minutes before Rhodri.
First, we convert Rhodri's travel time to hours by dividing the distance by his average speed:
Travel time for Rhodri = Distance / Speed = 5.5 miles / 22 mph = 0.25 hours
Since Megan arrives 5 minutes (which is 5/60 hours or 1/12 hours) earlier than Rhodri, we can calculate her travel time:
Megan's travel time = Rhodri's travel time - 5 minutes = 0.25 hours - (1/12 hours) = 0.25 - 0.08333 = 0.16667 hours
Now we can find the distance Megan cycles using her travel time and her average speed:
Distance Megan cycles = Megan's travel time * Megan's average speed = 0.16667 hours * 12 mph = 2 miles
Therefore, Megan cycles 2 miles to reach the swimming pool.