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# algebra

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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, 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?

Dec 1, 2022

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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

Dec 1, 2022