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Eva maintained an average speed of 35mph35\,\text{mph} for the first mm hours of her road trip. For the next nn hours of the trip, she drove at an average speed of 60mph60\,\text{mph}. Eva drove a total of 225225 miles in 4.54.5 hours. Which of the following systems of equations could be used to find how many miles Eva drove in the first mm hours of the trip?\newlineChoose 11 answer:\newline(A) m+n=225m+n=225\newline35m+60n=4.535m+60n=4.5\newline(B) m+n=4.5m+n=4.5\newline35m+60n=22535 m+60 n=225\newline(C) m+n=225m+n=225\newline60m+35n=4.560 m+35 n=4.5\newline(D) m+n=4.5m+n=4.5\newline60m+35n=22560 m+35 n=225

Full solution

Q. Eva maintained an average speed of 35mph35\,\text{mph} for the first mm hours of her road trip. For the next nn hours of the trip, she drove at an average speed of 60mph60\,\text{mph}. Eva drove a total of 225225 miles in 4.54.5 hours. Which of the following systems of equations could be used to find how many miles Eva drove in the first mm hours of the trip?\newlineChoose 11 answer:\newline(A) m+n=225m+n=225\newline35m+60n=4.535m+60n=4.5\newline(B) m+n=4.5m+n=4.5\newline35m+60n=22535 m+60 n=225\newline(C) m+n=225m+n=225\newline60m+35n=4.560 m+35 n=4.5\newline(D) m+n=4.5m+n=4.5\newline60m+35n=22560 m+35 n=225
  1. Understand the problem: Understand the problem.\newlineEva drove for a total of 4.54.5 hours and covered 225225 miles. She drove for mm hours at 3535 mph and for nn hours at 6060 mph. We need to find a system of equations that represents this situation.
  2. Set up time equation: Set up the first equation based on the total time.\newlineEva drove for mm hours and then for nn hours, which together should add up to the total time of the trip, which is 4.54.5 hours. So the first equation should be:\newlinem+n=4.5m + n = 4.5
  3. Set up distance equation: Set up the second equation based on the total distance.\newlineEva drove mm hours at 3535 mph and nn hours at 6060 mph. The distance she covered in the first mm hours is 35m35m miles, and the distance she covered in the next nn hours is 60n60n miles. The total distance is 225225 miles. So the second equation should be:\newline35m+60n=22535m + 60n = 225
  4. Identify correct system: Identify the correct system of equations.\newlineLooking at the choices given, we need to find the one that matches the two equations we have set up in Steps 22 and 33. The correct system of equations is:\newlinem+n=4.5m + n = 4.5\newline35m+60n=22535m + 60n = 225
  5. Choose correct answer: Choose the correct answer.\newlineThe correct answer is the one that matches the system of equations we found in Step 44. This corresponds to choice (B):\newline(B) m+n=4.5m + n = 4.5\newline 35m+60n=22535m + 60n = 225