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?
also, it would be great you could tell me how you got the answer, rather than giving me a straight answer , as I am trying to learn.
is there a picture or more information? There is not enough information to solve this question. How far is the cafe from the boba shop? How long did she go uphill, flatground, and downhill? There is not enough info to solve this
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
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.
Let's say the distance between the café and the boba shop is d, and Carissa walks the same distance in reverse on her way back.
Let's break the trip down into three parts: walking uphill, walking across flat ground, and walking downhill.
When walking uphill, Carissa walks at a speed of 100 meters per hour, so it takes her d/100 hours to complete this part of the trip.
When walking across flat ground, Carissa walks at a speed of 120 meters per hour, so it takes her d/120 hours to complete this part of the trip.
When walking downhill, Carissa walks at a speed of 150 meters per hour, so it takes her d/150 hours to complete this part of the trip.
So, the total time for the round trip is:
d/100 + d/120 + d/150 + d/100 + d/120 + d/150 = (11/600)d
To find the average speed, we need to divide the total distance (2d) by the total time, which is (11/600)d:
average speed = 2d / ((11/600)d) = 1200 / 11 ≈ 109.1 meters per hour
Therefore, Carissa's average speed during the entire round trip is approximately 109.1 meters per hour.
We can use the formula for average speed, which is the total distance traveled divided by the total time taken. Let's call the total distance traveled "d".
Since Carissa took the same route both ways, the distance traveled uphill is the same in both directions, and the same is true for the distance traveled downhill and across flat ground. So, the total distance traveled uphill is 2d/3, the total distance traveled across flat ground is d/3, and the total distance traveled downhill is 2d/3.
The time taken to travel uphill at 100 meters per hour is 2d/3 * (1 hour/100 meters) = 2d/(300 meters), the time taken to travel across flat ground at 120 meters per hour is d/3 * (1 hour/120 meters) = d/(360 meters), and the time taken to travel downhill at 180 meters per hour is 2d/3 * (1 hour/180 meters) = 2d/540 meters.
The total time taken is 2d/(300 meters) + d/(360 meters) + 2d/540 meters = (12d + 12d + 10d)/(180 meters) = 24d/180 meters = 4d/30 meters.
The average speed during the entire round trip is d/(4d/30 meters) = 30/4 = 7.5 meters per hour.
If her speed uphill, downhill and on flat ground given in the question represents the distance between the Boba shop and the Cafe', then the time taken to walk from the Shop to Cafe' is 3 hours. But, walking back from the Cafe' to the Shop, the 250-meter downhill becomes 250 m uphill ! Her speed uphill is 100 m/h. Therefore, it will take her: 2.5 hours to climb the 250 m. The 180 meters on flat ground will take the same time as 1 hour. The 100-meter uphill becomes 100 meters downhill. Since her speed downhill is 250 m/h, then she can cover that 100 meters in: 100 / 250 ==0.4 of an hour.
So, total distance is: 2 * [100 + 180 + 250] ==1,060 meters
Total time ==[1 + 1 + 1 + 2.5 + 1 + 0.4 ]==6.9 hours
Then, her average speed ==1,060 / 6.9 ==153.623 m / hour