Carissa the chessplayer is a very, very slow walker. In fact, she walks at 100 meters per hour when walking uphill, 180 meters per hour when walking across flat ground, and 250 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?
To answer this we need additional information, such as ...
suppose the 3 sections are each x m long
So the total distance walked = 6x
sum of the parts = x/100 + x/180 + x/250 + x/100 + x/180 + x/250
= x(2/100 + 2/250 + 2/180) = x(44/1125)
avg speed = total distance/ total time = 6x/(x(44/1125)) = appr 153.4
If my assumption is wrong, then there must be some more
information given to proceed.
It looks like the bot foolishly just averaged the 3 speeds.
To find Carissa's average speed during the entire round trip, we need to calculate the total distance she traveled and the total time it took her.
Let's assume the distance between the café and the boba shop is 'd' meters.
When Carissa walks uphill, her speed is 100 meters per hour. So, the time it takes her to walk from the café to the boba shop uphill is d/100 hours.
When Carissa walks across flat ground, her speed is 180 meters per hour. So, the time it takes her to walk from the boba shop to the café across flat ground is d/180 hours.
When Carissa walks downhill, her speed is 250 meters per hour. So, the time it takes her to walk from the café to the boba shop downhill is d/250 hours.
Similarly, the time it takes her to walk from the boba shop to the café uphill is d/100 hours.
Therefore, the total time for the round trip is:
(d/100) + (d/180) + (d/250) + (d/100)
To calculate the average speed, we divide the total distance by the total time:
Average Speed = (2d) / [(d/100) + (d/180) + (d/250) + (d/100)]
To simplify the equation, we can first find a common denominator for the denominators in the time equation:
Average Speed = (2d) / [(9d/900) + (5d/900) + (4d/1000) + (9d/900)]
Simplifying further, we get:
Average Speed = (2d) / [(27d + 45d + 36d + 18d) / 900]
Average Speed = (2d) / (126d / 900)
Average Speed = (2d) / (7d / 50)
Average Speed = (100d) / (7d)
Average Speed = 100/7 meters per hour
Therefore, Carissa's average speed during the entire round trip is 100/7 meters per hour.
To find Carissa's average speed during the entire round trip, we need to calculate the total distance covered and the total time taken.
Let's break down the round trip into two segments: from the café to the boba shop and from the boba shop back to the café.
1. Café to Boba Shop:
- Carissa walks uphill, so her speed is 100 meters per hour.
- Let's assume the distance between the café and the boba shop is "d" meters.
- So, the time taken to walk uphill from the café to the boba shop is d / 100 hours.
2. Boba Shop to Café:
- Carissa walks downhill, so her speed is 250 meters per hour.
- The distance from the boba shop back to the café is also "d" meters.
- Hence, the time taken to walk downhill from the boba shop to the café is d / 250 hours.
Now, let's calculate the total time taken for the round trip:
- The total time taken (in hours) is given by the sum of the time taken for each segment:
Total time = (d / 100) + (d / 250)
To find the average speed, we need to calculate the total distance covered in the round trip. Since Carissa travels the same distance on the way back, the total distance is 2d.
Now, we can calculate the average speed:
- Average speed = Total distance / Total time
= 2d / [(d / 100) + (d / 250)]
Simplifying the expression:
- Average speed = 2d * (1 / (d / 100 + d / 250))
= 2 / (1 / 100 + 1 / 250)
= 2 / (0.01 + 0.004)
= 2 / 0.014
≈ 142.857 meters per hour
Therefore, Carissa's average speed during the entire round trip is approximately 142.857 meters per hour.