Question

Ilya and Anya each can run at a speed of 7.30 mph and walk at a speed of 4.00 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.

Answer 1

a)0.9675 h

b)5.168 mph

c)0.885 h

d)5.65 mph

Step-by-step explanation:

The distance travelled by a moving object can be calculated as the velocity multiplied by the time, for this problem we can divide the problem in two stages, one where the are walking and another where they run,

Considering the total time for Anya is
`t_(a)`:

She first walks for half the distance (2.5 miles) so:

`2.5 miles=V_(w)*t_(a1)`

Solving for
`t_(a1)`:

`t_(a1)=(2.5miles)/(V_(w))=(2.5miles)/(4 mph)=0.625 h`

Then she runs the other half of the distance:

`2.5 miles=V_(r)*t_(a2)`

`t_(a2)=(2.5miles)/(V_(r))=(2.5miles)/(7.3 mph)=0.3425 h`

Adding this two durations we have the total time it takes for Anya to cover the distance:

`t_(a)=0.3425 h+0.625 h=0.9675 h`

The average velocity can be calculated as the total distance divided by the total time:

`V_(a-av) =(5 miles)/(0.9675 h) =5.168 mph`

Considering the total time for Ilya is
`t_(I)`:

She first walks for half the time so:

`d_(I1)=V_(w)*t_(I)/2`

Where
`V_(w)` is the velocity when walking (same for both people). On the second half she runs:

`d_(I2)=V_(r)*t_(I)/2`

This two distances must sum the total distance 5 miles, so:

`d_(I2)+d_(I2)=5 miles`

replacing the expressions above:

`V_(w)*t_(I)/2+V_(r)*t_(I)/2=(V_(w)+V_(r))*t_(I)/2=5 miles`

`t_(I)=(5miles*2)/(V_(w)+V_(r))=(10 miles)/(4mph+7.3mph)=0.885 h`

so it takes Ilya 0.885 hours to to cover the distance

The average velocity can be calculated as the total distance divided by the total time:

`V_(I-av) =(5 miles)/(0.885 h) =5.65 mph`