Question

Carlos and Maria drove a total of 217 miles in 4.1 hours. Carlos drove the first part of the trip and averaged 52 miles per hour. Maria drove the remainder of the trip and averaged 54 miles per hour. For approximately how many hours did Maria drive? Round your answer to the nearest tenth if necessary. 2.2 hours 1.1 hours 1.9 hours 1.5 hours

Answer 1

M = hours driven by Maria

c = hours driven by Carlos

since we know that Carlos was driving at an average of 52 mph, then in 1 hour he drove 52 miles, in 2 hours he drove 2*52 miles in "c" hours he drove c*52 miles or 52c.

Maria on the other hand is faster and does 54 mph, in 1 hour she does 1 * 54 miles, and on 2 hours she does 2 * 54 miles and in "m" hours she does m * 54 miles or 54m.

now, we know the total amount of miles they both drove is 217, so whatever "m" and "c" are we know that 54m + 52c = 217.

we also know it took 4.1 for the whole trip, so m + c = 4.1.

$\bf \begin{cases} m+c=4.1\implies \boxed{c}=4.1-m\\ 54m+52c=217\\ -------------\\ 54m+52\left( \boxed{4.1-m} \right)=217 \end{cases} \\\\\\ 54m-52m+213.2=217\implies 2m=3.8 \\\\\\ m=\cfrac{3.8}{2}\implies m=1.9$

so Maria drove for 1.9 hours.

How many hours did Carlos drive for?  well, c = 4.1 - m.