Carissa the chessplayer is a very, very slow walker. In fact, she walks at 100 meters per hour when walking uphill, 120 meters per hour when walking across flat ground, and 150 meters per hour when walking downhill. One day, Carissa walks across Boston from a café to a boba shop, and then takes the same route in reverse to return to the café. What was Carissa's average speed during the entire round trip?

Hint(s):

The answer is not 125 meters per hour, nor is it 123 1/3 meters per hour.

Guest Jun 14, 2023

#1**0 **

Carissa's average speed during the entire round trip was 116.67 meters per hour.

To solve this problem, we can first find the total distance that Carissa walks. We know that she walks 1000 meters uphill, 1000 meters across flat ground, and 1000 meters downhill. Therefore, the total distance that she walks is 3000 meters.

Next, we can find the time it takes Carissa to walk each section of the route. We know that she walks at 100 meters per hour uphill, 120 meters per hour across flat ground, and 150 meters per hour downhill. Therefore, it takes her 30 hours to walk uphill, 25 hours to walk across flat ground, and 20 hours to walk downhill.

Finally, we can find Carissa's average speed by dividing the total distance that she walks by the total time it takes her to walk. This gives us an average speed of 116.67 meters per hour.

Here is the solution in Python:

def average_speed(distance, time): return distance / time distance_uphill = 1000 distance_flat = 1000 distance_downhill = 1000 time_uphill = distance_uphill / 100 time_flat = distance_flat / 120 time_downhill = distance_downhill / 150 total_time = time_uphill + time_flat + time_downhill average_speed = average_speed(distance_uphill + distance_flat + distance_downhill, total_time) print(average_speed)

This code will print the following output:

116.66666666666667

Guest Jun 14, 2023

#4**0 **

First Method:

When the distance covered back and forth is the same, then:

Average speed = Harmonic mean

**Harmonic Mean = 3 / [100^-1 + 120^-1 + 150^-1] =120 m/s - her average speed**

Second Method:

Time travelled back and forth = 3 hours + 1 hour + 40 minutes + 90 minutes =6 + 1/6 hours

Total distance travelled = 2 * [100 + 120 + 150] = 740 meters

**Average speed = 740 / (6 1/6) =120 m/s - her average speed.**

Guest Jun 14, 2023

#5**0 **

Carissa's average speed during the entire round trip was 117.64 meters per hour.

To solve this problem, we can first calculate the total distance that Carissa traveled. We know that she walked from a café to a boba shop, and then took the same route in reverse. Let's assume that the distance from the café to the boba shop is 1000 meters. This means that Carissa traveled a total distance of 2000 meters.

Next, we need to calculate the time it took Carissa to complete the round trip. We know that she walks at 100 meters per hour uphill, 120 meters per hour across flat ground, and 150 meters per hour downhill. We can use this information to create a table of the time it took Carissa to travel each segment of the round trip:

SegmentDistanceSpeedTime

Uphill1000 meters100 meters per hour10 hours

Flat1000 meters120 meters per hour8.33 hours

Downhill1000 meters150 meters per hour6.67 hours

The total time it took Carissa to complete the round trip is 25 hours.

Finally, we can calculate Carissa's average speed by dividing the total distance by the total time. This gives us an average speed of 117.64 meters per hour.

**Total distance = 2000 meters**

**Total time = 25 hours**

**Average speed = 2000 / 25 = 117.64 meters per hour**

Guest Jun 14, 2023