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# Algebra help due TODAY!! (3 hours)

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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? (the answer is not 125 or 123 1/2)
Apr 6, 2023

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Apr 6, 2023
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Carissa walks at different speeds on flat ground, uphill, and downhill. Her average speed is not the average of these speeds, because she spends more time walking uphill and downhill than she does walking on flat ground.

To calculate Carissa's average speed, we first need to calculate the total time she takes to walk from the café to the boba shop and back. Let's say the distance between the café and the boba shop is d. Carissa walks at a speed of 100 meters per hour when walking uphill, so it takes her d/100 hours to walk this distance. She then walks at a speed of 120 meters per hour when walking across flat ground, so it takes her d/120 hours to walk this distance. Finally, she walks at a speed of 150 meters per hour when walking downhill, so it takes her d/150 hours to walk this distance. Therefore, the total time for the round trip is:

d/100 + d/120 + d/150

To find the average speed, we need to divide the total distance (2d) by the total time, which is d/100 + d/120 + d/150:

average speed = 2d / (d/100 + d/120 + d/150)

= 1200 / (11/600)

≈ 109.1 meters per hour

Therefore, Carissa's average speed during the entire round trip is approximately 109.1 meters per hour.

Apr 6, 2023