Question

Ilya and Anya each can run at a speed of 8.90mph and walk at a speed of 3.80mph . They set off together on a route of length 5.00miles. 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 ?
Express your answer numerically, in minutes.
b)Find Anya's average speed.
Express Anya's average speed save,Anya numerically, in miles per hour
C)How long does it take Ilya to cover the distance?
Express the time tIlya taken by Ilya numerically, in minutes.
d)Now find Ilya's average speed.
Express Ilya's average speed save,Ilya numerically, in miles per hour

Answer 1

Anya takes 56.33 minutes to travel 5.00 miles with an average speed of 5.33 mph, while Ilya takes 61.96 minutes with an average speed of 4.84 mph.

Step-by-step explanation:

To calculate Anya's travel time for the 5.00 miles, we consider that she walks half the distance (2.5 miles) at 3.80 mph and runs the other half at 8.90 mph:

Walking time = 2.5 miles / 3.80 mph = 0.6579 hours.

Running time = 2.5 miles / 8.90 mph = 0.2809 hours.

Total time in hours = 0.6579 + 0.2809 = 0.9388 hours.

Total time in minutes = 0.9388 hours × 60 minutes/hour = 56.33 minutes.

To find Anya's average speed, we divide the total distance by the total time:

Average speed = 5.00 miles / 0.9388 hours = 5.33 mph.

To calculate Ilya's travel time, we assume half the total time is spent walking and the other half running. If the total time taken is T, then we have:

T/2 in hours × 3.80 mph + T/2 in hours × 8.90 mph = 5.00 miles.

Solving for T gives us T = 1.0326 hours or 61.96 minutes.

For Ilya's average speed, we simply divide the total distance by the total time:

Average speed = 5.00 miles / 1.0326 hours ≈ 4.84 mph.

Answer 2

Part a)

`T = 0.94 hours`

Part b)

`v_(avg) = 5.32 mph`

Part c)

`T = 0.79 h`

Part d)

`v_(avg) = 6.35 mph`

Step-by-step explanation:

Speed while she is running = 8.90 mph

speed while she walk = 3.80 mph

Part a)

Anya walks half the distance

so time to walk

`t_1 = (2.5)/(3.80) = 0.66 h`

time to cover the distance while she run

`t_2 = (2.5)/(8.90) = 0.28 h`

total time to cover the distance

`T = t_1 + t_2`

`T = 0.94 hours`

Part b)

Average speed is given as

`v_(avg) = (d)/(t)`

`v_(avg) = (5.00 miles)/(0.94)`

`v_(avg) = 5.32 mph`

Part c)

Half the time Llya walks and next half the time she runs

so total distance is given as

`d = v_1(T/2) + v_2(T/2)`

so we have

`5.00 = 8.90(T/2) + 3.80(T/2)`

`T = 0.79 h`

Part d)

Average speed is given as

`v_(avg) = (d)/(t)`

`v_(avg) = (5.00 miles)/(0.79)`

`v_(avg) = 6.35 mph`