Ilya and Anya each can run at a speed of 8.60 mph and walk at a speed of 3.30 mph . They set off together on a route of length 5.00 miles . Anya walks half of the distance and runs the other half, while Ilya walks half of the time and runs the other half.
To solve this problem, we need to determine the total time it takes for both Ilya and Anya to complete the 5-mile route.
First, let's calculate the time it takes for Anya to walk half of the distance (2.5 miles). We can use the formula Distance = Speed × Time to find the time taken to walk:
Time1 = Distance1 / Speed1
Time1 = 2.5 miles / 3.30 mph
Next, let's calculate the time it takes for Anya to run the other half of the distance (2.5 miles):
Time2 = Distance2 / Speed2
Time2 = 2.5 miles / 8.60 mph
The total time taken by Anya is the sum of Time1 and Time2:
Total Time Anya = Time1 + Time2
Now, let's calculate the time it takes for Ilya to walk half of the time. Since the walking speed is the same as Anya's, Ilya's walking time will also be equal to Time1.
The remaining time for Ilya is the total time minus the walking time:
Remaining Time Ilya = Total Time Anya - Time1
Now, let's calculate the time it takes for Ilya to run the remaining distance (2.5 miles). We can use the remaining time and the running speed:
Time3 = Remaining Distance / Speed2
Time3 = 2.5 miles / 8.60 mph
Finally, the total time taken by Ilya is the sum of Time1 and Time3:
Total Time Ilya = Time1 + Time3
To find the total time taken by both Ilya and Anya together, we can add their individual times:
Total Time = Total Time Anya + Total Time Ilya
Now, let's substitute the given values into the equations and calculate the final answer.