Respuesta :
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.
[tex]\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[/tex]
so Maria drove for 1.9 hours.
How many hours did Carlos drive for? well, c = 4.1 - m.
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.
[tex]\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[/tex]
so Maria drove for 1.9 hours.
How many hours did Carlos drive for? well, c = 4.1 - m.
