Ilya and Anya each can run at a speed of 8.00 mph and walk at a speed of 3.50 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.

1) Find Anya's average speed.

2) How long does it take Ilya to cover the distance?

3) Now find Ilya's average speed.

1. d = r*t1 = 2.5, 3.5 * t1 = 2.5, t1 = 0.714 Hours.

r*t2 = 2.5, 8 * t2 = 2.5, t2 = 0.3125 Hours.

Average Speed = 5/(t1+t2).

2. 3.5 * 0.5t + 8 * 0.5t = 5,
5.75t = 5, t = 0.870 Hours.

3. Average Speed = 5/t.

To find the answers to the questions, we can use the formula: average speed = total distance / total time.

1) To find Anya's average speed:
Any distance that Anya covers while walking is 5 miles (half of the total distance).
Time taken to walk half of the distance = distance / speed = 5 miles / 3.50 mph = 1.43 hours.

Any distance that Anya covers while running is also 5 miles (half of the total distance).
Time taken to run the other half of the distance = distance / speed = 5 miles / 8.00 mph = 0.63 hours.

Total time taken by Anya = time taken to walk + time taken to run = 1.43 hours + 0.63 hours = 2.06 hours.

Anya's average speed = total distance / total time = 5 miles / 2.06 hours = 2.43 mph.

2) To find the time taken by Ilya to cover the distance:
Since Ilya walks for half of the time and walks at a speed of 3.50 mph, the time taken to walk half of the distance is the same as the time taken by Anya while walking, which is 1.43 hours.

Therefore, Ilya runs for the other half of the time. The time taken to run the other half of the distance is given by:
Time taken to run = total time - time taken to walk = 2.06 hours - 1.43 hours = 0.63 hours.

3) To find Ilya's average speed:
Total time taken by Ilya = time taken to walk + time taken to run = 1.43 hours + 0.63 hours = 2.06 hours.

Ilya's average speed = total distance / total time = 5 miles / 2.06 hours = 2.43 mph, which is the same as Anya's average speed.

To find the answers to these questions, we need to use the formula for average speed, which is:

Average Speed = Total Distance / Total Time

1) To find Anya's average speed, we first need to determine the total time it takes for her to cover the distance. Given that she walks half the distance and runs the other half, we can calculate:

Time taken to walk = Distance walked / Walking speed
Time taken to run = Distance run / Running speed

Since she covers the same distance walking and running:

Time taken to walk = Time taken to run

Thus, the total time taken by Anya is:

Total Time = Time taken to walk + Time taken to run
= (Distance walked / Walking speed) + (Distance run / Running speed)
= (2.5 miles / 3.5 mph) + (2.5 miles / 8 mph)

To find Anya's average speed, we can substitute the total time into the formula:

Anya's Average Speed = Total Distance / Total Time
= 5 miles / (2.5 miles / 3.5 mph + 2.5 miles / 8 mph)

2) To find how long it takes Ilya to cover the distance, we need to determine the total time. Since Ilya walks half the time and runs the other half, we can calculate the time taken for each:

Time taken to walk = Distance walked / Walking speed
Time taken to run = Distance run / Running speed

Again, since he covers the same distance walking and running:

Time taken to walk = Time taken to run

Thus, the total time taken by Ilya is:

Total Time = Time taken to walk + Time taken to run
= (Distance walked / Walking speed) + (Distance run / Running speed)
= (2.5 miles / 3.5 mph) + (2.5 miles / 8 mph)

3) To find Ilya's average speed, we divide the total distance by the total time:

Ilya's Average Speed = Total Distance / Total Time
= 5 miles / (2.5 miles / 3.5 mph + 2.5 miles / 8 mph)