Ilya and Anya each can run at a speed of 7.80 and walk at a speed of 3.20 . They set off together on a route of length 5.00 . 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
How long does it take Anya to cover the distance of 5.00 ?
Express your answer numerically, in minutes.
Part B
Find Anya's average speed.
Express Anya's average speed numerically, in miles per hour.
Part C
How long does it take Ilya to cover the distance?
Express the time taken by Ilya numerically, in minutes.
Now find Ilya's average speed.
Express Ilya's average speed numerically, in miles per hour.
Part A: To calculate the time it takes Anya to cover a distance of 5.00, we need to consider that she walks half the distance and runs the other half.
The time Anya spends walking is determined by the distance she walks divided by her walking speed:
Time walking = (distance/2) / walking speed
Time walking = (5.00/2) / 3.20
Time walking = 5.00/6.40
Time walking = 0.78125 hours
To express the time in minutes, we multiply by 60:
Time walking = 0.78125 * 60
Time walking = 46.875 minutes
Therefore, it takes Anya 46.875 minutes to cover the distance of 5.00.
Part B: To find Anya's average speed, we need to calculate the total distance she covers divided by the total time taken.
The total distance is 5.00 since she covers that distance.
The total time is the time spent walking plus the time spent running. Since she walks half the distance and runs the other half, the time spent running will be the same as the time spent walking.
Total time = Time walking + Time running = 46.875 + 46.875 = 93.75 minutes
Average speed = total distance / total time
Average speed = 5.00 / (93.75/60)
Average speed = 5.00 / 1.5625
Average speed = 3.2 miles per hour
Therefore, Anya's average speed is 3.2 miles per hour.
Part C: To calculate the time it takes Ilya to cover the distance of 5.00, we need to consider that he walks half the time and runs the other half.
The time Ilya spends walking is half of the total time taken:
Time walking = Total time / 2 = 93.75 / 2 = 46.875 minutes
To express the time in hours, we divide by 60:
Time walking = 46.875 / 60 = 0.78125 hours
To express the time in minutes, we multiply by 60:
Time walking = 0.78125 * 60 = 46.875 minutes
Therefore, it takes Ilya 46.875 minutes to cover the distance of 5.00.
Now, let's calculate Ilya's average speed:
Since Ilya walks for half the time and runs for the other half, his total time is the same as Anya's, which is 93.75 minutes.
Average speed = total distance / total time
Average speed = 5.00 / (93.75/60)
Average speed = 5.00 / 1.5625
Average speed = 3.2 miles per hour
Therefore, Ilya's average speed is also 3.2 miles per hour.
Part A:
To find out how long it takes Anya to cover the distance of 5.00, we need to calculate the time taken for walking and running separately.
Walking Time:
Anya walks half the distance, which is 5.00 / 2 = 2.50 miles. Since her walking speed is 3.20 miles per hour, the time taken for walking is 2.50 / 3.20 = 0.78125 hours.
Running Time:
Anya also runs half the distance, which is 5.00 / 2 = 2.50 miles. Since her running speed is 7.80 miles per hour, the time taken for running is 2.50 / 7.80 = 0.32051 hours.
Therefore, the total time taken by Anya to cover the distance is 0.78125 + 0.32051 = 1.10176 hours.
Converting to minutes: 1.10176 * 60 = 66.106 minutes.
So, it takes Anya approximately 66.106 minutes to cover the distance of 5.00.
Part B:
Anya's average speed can be found by dividing the total distance covered (5.00 miles) by the total time taken (1.10176 hours).
Average Speed = Distance / Time = 5.00 / 1.10176 = 4.5379 mph.
Therefore, Anya's average speed is approximately 4.5379 miles per hour.
Part C:
Similar to Anya, we need to calculate the time taken for walking and running separately.
Walking Time:
Ilya walks half the distance, which is 5.00 / 2 = 2.50 miles. Since his walking speed is 3.20 miles per hour, the time taken for walking is 2.50 / 3.20 = 0.78125 hours.
Running Time:
Ilya also runs half the distance, which is 5.00 / 2 = 2.50 miles. Since his running speed is 7.80 miles per hour, the time taken for running is 2.50 / 7.80 = 0.32051 hours.
Therefore, the total time taken by Ilya to cover the distance is 0.78125 + 0.32051 = 1.10176 hours.
Converting to minutes: 1.10176 * 60 = 66.106 minutes.
So, it takes Ilya approximately 66.106 minutes to cover the distance of 5.00.
Ilya's average speed can be found by dividing the total distance covered (5.00 miles) by the total time taken (1.10176 hours).
Average Speed = Distance / Time = 5.00 / 1.10176 = 4.5379 mph.
Therefore, Ilya's average speed is approximately 4.5379 miles per hour.
PART A - 63.7 minutes
PART B- 4.71 mph
PART C- 52.2
PART D- 5.75