Answer:
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:
Hi there!
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.
