Ilya and Anya each can run at a speed of 7.20 mph and walk at a speed of 3.40 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.
How long does it take Anya to cover the distance of 5.00 miles ?
Find Anya's average speed.
How long does it take Ilya to cover the distance?
Now find Ilya's average speed.
Anya: t = 2.5/7.2 + 2.5/3.4 = ___ hr
avg speed = 5/t km/hr
Ilya: 7.2*t/2 + 3.4*t/2 = 5.0
avg speed: 5/t km/hr
To determine how long it takes Anya to cover the distance of 5.00 miles, we need to calculate the time she spends walking and running separately. We can then add those times together to get the total time.
Anya walks half of the distance, which is 5.00 / 2 = 2.50 miles. To find the time it takes her to walk this distance, we can use the formula:
Time = Distance / Speed
Time walking = 2.50 miles / 3.40 mph = 0.735 hours
Anya also runs the other half of the distance, which is also 2.50 miles. To find the time it takes her to run this distance, we can use the same formula:
Time running = 2.50 miles / 7.20 mph = 0.347 hours (rounded to 3 decimal places)
Now, let's add the two times together to find the total time it takes Anya to cover the 5.00 miles:
Total time = Time walking + Time running
Total time = 0.735 hours + 0.347 hours = 1.082 hours (rounded to 3 decimal places)
Therefore, it takes Anya approximately 1.082 hours to cover the distance of 5.00 miles.
Now let's find Anya's average speed:
Average speed = Total distance / Total time
We already know the total distance is 5.00 miles, and we calculated the total time as 1.082 hours.
Average speed = 5.00 miles / 1.082 hours = 4.624 mph (rounded to 3 decimal places)
Therefore, Anya's average speed is approximately 4.624 mph.
For Ilya, we need to calculate the time he spends walking and running separately, just like we did for Anya.
Ilya walks for half of the time, which is 0.735 hours (the same time Anya spent walking).
Ilya also runs for the other half of the time, which is also 0.735 hours.
Therefore, it takes Ilya approximately 0.735 hours to cover the distance of 5.00 miles.
Now, let's find Ilya's average speed:
Average speed = Total distance / Total time
Again, the total distance is 5.00 miles, and we calculated the total time as 0.735 hours.
Average speed = 5.00 miles / 0.735 hours = 6.803 mph (rounded to 3 decimal places)
Therefore, Ilya's average speed is approximately 6.803 mph.