# Mathematics - Other

Florence and Larry race on a windy day: 100 yards with the wind, they instantly turn around, and race 100 yards back against the wind. Larry is unaffected by the wind, but Florence only goes 90% as fast running against the wind as when running with no wind. Running with the wind improves Florence's no-wind speed by 10%. On a day with no wind, Florence and Larry tie in a 100-yard race. Who wins the windy-day race, and by how much?

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

Let the speed of Florence in no wind be x yards per minute and Larry's be y yards per minute.

For Larry, since he is unaffected by wind, total time taken = distance/speed

= (100 + 100)/y = 200/y minutes.

For Florence, speed against the wind is 0.9x and speed with the wind is 1.1x.

Total time taken by her = distance/speed

= (100/0.9x) + (100/1.1x) = (1000/9x) + (1000/11x)

= 20000/99x ?[By LCM]

Since on a no wind day, they tie in the race, 200/x = 200/y

Therefore, x = y .

On a windy day, Larry's time = 200/y and Florence's time = 20000/99x

= 20000/99y = 202.02/y.

Larry wins the race by a time lead of 1%.

Â© BrainMass Inc. brainmass.com December 24, 2021, 7:51 pm ad1c9bdddf>https://brainmass.com/math/basic-algebra/algebra-word-problems-wins-race-224323