Ilya and Anya each can run at a speed of 8.00 mph and walk at a speed of 3.20 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?
Express your answer numerically, in minutes.
b. Find Anya's average speed.
Express Anya's average speed save, Anya numerically, in miles per hour
c. How long does it take Ilya to cover the distance?
Express the time Ilya taken by Ilya numerically, in minutes.
d. Now find Ilya's average speed.
Express Ilya's average speed save, Ilya numerically, in miles per hour

a) T = 1.094 hours = 65.63 minutes

b) 4.57 mph

c) t = 0.893 hour = 53.57 minutes

d) 5.60 mph

Explanation:

Anya walks half of the distance and runs half of the distance.

Meaning Anya runs 2.5 miles and walks 2.5 miles

Speed = distance/time; time = distance/speed

Running speed = 8 mph, walking speed = 3.2 mph

Running time for Anya, = 2.5/8 = 0.3125 hour

Walking time for Anya = 2.5/3.2 = 0.78125 hour

Total time taken to cover 5 miles = 1.09375 hours = 65.63 minutes

b) Average speed = total distance covered/total time taken = 5/1.09375 = 4.57 mph

c) Ilya splits the total time adequately even between walking and running.

Let total time taken to cover 5 miles be t,

Running time = t/2 and walking time = t/2

Running distance = running speed × running time = 8 × t/2 = 4t

Walking distance = walking speed × walking time = 3.2 × t/2 = 1.6t

Total distance = 4t + 1.6t = 5

5.6t = 5,

t = 0.893 hour = 53.57 minutes

d) Average speed = total distance covered/total time taken = 5/0.893 = 5.60 mph