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Mrs. Gunner drove from Own Sound to Ottawa, a distance of 550 Km. Mrs. Gunner can drive at 70 Km/h for part of trip, and 85 Km/h for the remainder of the trip. if the trip takes 7 hours , how far did she drive at 70 Km/hand how far did she drive at 85 Km/h

Respuesta :

mhanifa

210 km at 70 km/h and

340 km at 85 km/h

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We have a total distance of 550 Km that Mrs. Gunner must drive and a total time of 7 hours.

To solve this problem, we can set up two equations based on the distance covered at each speed and the corresponding times.

Let x represent the distance traveled at 70 km/h and y represent the distance traveled at 85 km/h. Since the total distance is 550 km, we can write our first equation as:

  • x + y = 550

The time taken to travel distance x at 70 km/h is x/70 and the time to travel distance y at 85 km/h is y/85. Since the total time for the trip is 7 hours, our second equation is:

  • x/70 + y/85 = 7

Now we can solve this system of linear equations using substitution methods.

From the first equation, we can express y in terms of x:

  • y = 550 - x

Substituting this into our second equation, we get:

  • x/70 + (550 - x)/85 = 7

Solving for x, we get:

  • 85x + 70(550 - x) = 7*70*85
  • 15x + 38500 = 41650
  • 15x = 3150
  • x = 210 km

Now we can calculate the value of y using the first equation:

  • y = 550 - 210 = 340 km

Therefore, Mrs. Gunner drove 210 km at 70 km/h and 340 km at 85 km/h.

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