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?
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.
