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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 relates the time and distance for each part of the trip.
  2. Set up first equation: Set up the first equation based on the total time.\newlineThe total time driven was 4.54.5 hours, which is the sum of the time driven at 3535 mph (mm hours) and the time driven at 6060 mph (nn hours). Therefore, the first equation is:\newlinem+n=4.5m + n = 4.5
  3. Set up second equation: Set up the second equation based on the total distance.\newlineThe total distance driven was 225225 miles. Eva drove mm hours at 3535 mph and nn hours at 6060 mph. The distance driven at 3535 mph is 35m35m and the distance driven at 6060 mph is 60n60n. The sum of these distances should equal the total distance driven, which is 225225 miles. Therefore, the second equation is:\newlinemm00
  4. Identify system of equations: Identify the correct system of equations.\newlineBased on the equations from Step 22 and Step 33, the correct system of equations is:\newlinem+n=4.5m + n = 4.5\newline35m+60n=22535m + 60n = 225\newlineThis corresponds to option (B).