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# 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.

Santino
4.5
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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