keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. each month, he wants to…

keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. each month, he wants to complete at least 36 miles but not more than 90 miles. the system of inequalities represents the number of hours he can walk, w, and the number of hours he can run, r, to reach his goal.\n3w + 6r ≥ 36\n3w + 6r ≤ 90\nwhich combination of hours can keitaro walk and run in a month to reach his goal?\n2 hours walking; 12 hours running\n4 hours walking; 3 hours running\n9 hours walking; 12 hours running\n12 hours walking; 10 hours running

keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. each month, he wants to complete at least 36 miles but not more than 90 miles. the system of inequalities represents the number of hours he can walk, w, and the number of hours he can run, r, to reach his goal.\n3w + 6r ≥ 36\n3w + 6r ≤ 90\nwhich combination of hours can keitaro walk and run in a month to reach his goal?\n2 hours walking; 12 hours running\n4 hours walking; 3 hours running\n9 hours walking; 12 hours running\n12 hours walking; 10 hours running

Answer

Explanation:

Step1: Comprobar la primera opción

Sustituir $w = 2$ y $r=12$ en $3w + 6r$. $3\times2+6\times12=6 + 72=78$. Como $36\leq78\leq90$, esta opción es válida.

Step2: Comprobar la segunda opción

Sustituir $w = 4$ y $r = 3$ en $3w+6r$. $3\times4+6\times3=12 + 18=30$. Pero $30<36$, no cumple la desigualdad $3w + 6r\geq36$.

Step3: Comprobar la tercera opción

Sustituir $w = 9$ y $r = 12$ en $3w+6r$. $3\times9+6\times12=27+72 = 99$. Pero $99>90$, no cumple la desigualdad $3w + 6r\leq90$.

Step4: Comprobar la cuarta opción

Sustituir $w = 12$ y $r = 10$ en $3w+6r$. $3\times12+6\times10=36 + 60=96$. Pero $96>90$, no cumple la desigualdad $3w + 6r\leq90$.

Answer:

2 horas caminando; 12 horas corriendo