Question
Matilde knows that, when driving her car from her office to her apartment, she spends a normal time of x minutes. In the last week, you have noticed that when driving at 50 mph (miles per hour), you arrive home 4 minutes earlier than normal, and when driving at 40 mph, you arrive home 5 minutes earlier later than normal. If the distance between your office and your apartment is y miles, calculate x + y.
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Answer to a math question Matilde knows that, when driving her car from her office to her apartment, she spends a normal time of x minutes. In the last week, you have noticed that when driving at 50 mph (miles per hour), you arrive home 4 minutes earlier than normal, and when driving at 40 mph, you arrive home 5 minutes earlier later than normal. If the distance between your office and your apartment is y miles, calculate x + y.
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Cuando Matilde conduce a 50 mph, tarda (x - 4) minutos o ((x - 4)/60) horas. Entonces, tenemos la ecuación:
(y = 50 * (x - 4) / 60)
Cuando Matilde conduce a 40 mph, tarda (x + 5) minutos o ((x + 5)/60) horas. Entonces, tenemos la ecuación:
(y = 40 * (x + 5) / 60)
Podemos resolver este sistema de ecuaciones para encontrar los valores de (x) y (y).
Multiplicando la primera ecuación por 60 se obtiene:
(60 años = 50x - 200)
Multiplicando la segunda ecuación por 60 se obtiene:
(60 años = 40x + 200)
Restando la segunda ecuación de la primera se obtiene:
(0 = 10x - 400)
Resolviendo para (x) se obtiene:
(x = 40) minutos
Sustituyendo (x = 40) en la primera ecuación se obtiene:
(y = 50 * (40 - 4) / 60 = 30) millas
Por tanto, (x + y = 40 + 30 = 70). Entonces, la suma de (x) y (y) es 70.
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