Ilya and Anya each can run at a speed of 8.10 mph and walk at a speed of 3.90 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. a) How long does it take Anya to cover the distance of 5.00miles?

b) Find Anya's average speed.

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

d) Now find Ilya's average speed.

a) It takes Anya 0.950 h to cover the distance of 5.00 mi.

b) Anya's average speed is 5.26 mi/h.

c) It takes Ilya 0.833 h to cover the distance.

d) Ilya's average speed is 6.00 mi/h.

Explanation:

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a) The equation of traveled distance at constant speed is the following:

d = v · t

where:

d = traveled distance.

v = speed.

t = time.

Anya walks half of the distance (2.50 mi), so, using the equation of traveled distance we can obtain the time:

d/v = t

2.50 mi / 3.90 mi/h = t

t = 0.641 h

For the other half of the distance, she runs:

d/v = t

2.50 mi / 8.10 mi/h = t

t = 0.309 h

Then, it takes Anya (0.309 h + 0.641 h) 0.950 h to cover the distance of 5.00 mi.

b) The average speed is calculated as the traveled distance over the time it takes to travel that distance:

v = d/t

v = 5.00 mi / 0.950 h

v = 5.26 mi/h

Anya's average speed is 5.26 mi/h.

c) Let's write the equations of speed for Ilya. She walks a distance d1 for half of the total time. Then:

v = d/t

3.90 mi/h = d1 / t/2

Solving for d1:

3.90 mi/h · t/2 = d1

And then, she runs a distance d2 for the other half of the time:

8.10 mi/h = d2 / t/2

8.10 mi/h · t/2 = d2

We know that d1 + d2 = 5.00 mi, then:

3.90 mi/h · t/2 + 8.10 mi/h · t/2 = 5.00 mi

6.00 mi/h · t = 5.00 mi

t = 5.00 mi / 6.00 mi/h

t = 5/6 h

It takes Ilya 0.833 h to cover the distance.

d) The average can now be calculated:

v = 5.00 mi / 5/6 h

v = 6.00 mi/h

Ilya's average speed is 6.00 mi/h.