Question

Ilya and Anya each can run at a speed of 9.00 mph and walk at a speed of 3.80 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.

Part A ( I solved this part)

How long does it take Anya to cover the distance of 5.00 miles ?

Express your answer numerically, in minutes.

tAnya =
56.1

minutes
Part B ( I solved this part)

Find Anya's average speed.

Express Anya's average speed save,Anya numerically, in miles per hour.

save,Anya =
5.34

mph
Part C (NEED HELP)

How long does it take Ilya to cover the distance?

Express the time tIlya taken by Ilya numerically, in minutes.

tIlya = minutes
Part D (NEED HELP)

Now find Ilya's average speed.

Express Ilya's average speed save,Ilya numerically, in miles per hour.

Answer 1

For Anya

a) T = 0.936 hour = 56.1 minutes

b) 5.34 mph

For Ilya

c) t = 0.781 hour = 46.9 minutes

d) 6.40 mph

Step-by-step explanation:

a) 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 = 9 mph, walking speed = 3.8 mph

Running time for Anya, = 2.5/9 = 0.278 hour

Walking time for Anya = 2.5/3.8 = 0.658 hour

Total time taken to cover 5 miles = 0.278 + 0.658 = 0.936 hour = 56.1 minutes

b) Average speed = total distance covered/total time taken = 5/0.936 = 5.34 mph

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

Let total time taken to cover 5 miles be t,

Running time will be t/2 and walking time will be t/2

Speed = distance/time; distance = speed × time, So,

Running distance = running speed × running time = 9 × t/2 = 4.5t

Walking distance = walking speed × walking time = 3.8 × t/2 = 1.9t

Total distance = 4.5t + 1.9t = 5 miles

6.4t = 5,

t = 0.781 hour = 46.9 minutes

d) Average speed = total distance covered/total time taken = 5/0.781 = 6.40 mph