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.

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

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

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.