A mail carrier delivers mail on one of two different routes: a morning route or an afternoon route. Each workday the mail carrier is assigned one of these two routes.Last month the mail carrier delivered mail on the morning route 16 times and on the afternoon route 12 times, for a total distance traveled of 141 miles.This month the mail carrier delivered mail on the morning route 10 times and on the afternoon route 15 times, for a total distance traveled of 123.75 miles.What is the distance of the morning route in miles? A. 4.75 mi B. 5.00 mi C. 5.25 mi D. 6.00 mi
Question
A mail carrier delivers mail on one of two different routes: a morning route or an afternoon route. Each workday the mail carrier is assigned one of these two routes.Last month the mail carrier delivered mail on the morning route 16 times and on the afternoon route 12 times, for a total distance traveled of 141 miles.This month the mail carrier delivered mail on the morning route 10 times and on the afternoon route 15 times, for a total distance traveled of 123.75 miles.What is the distance of the morning route in miles? A. 4.75 mi B. 5.00 mi C. 5.25 mi D. 6.00 mi
Solution
To solve this problem, we can set up a system of linear equations. Let's denote the distance of the morning route as M and the distance of the afternoon route as A.
From the problem, we know that:
16M + 12A = 141 (equation 1) (from last month's data)
10M + 15A = 123.75 (equation 2) (from this month's data)
We can solve this system of equations by either substitution or elimination. Here, I'll use elimination.
First, let's multiply equation 1 by 10 and equation 2 by 16 to make the coefficients of M the same in both equations:
160M + 120A = 1410 (equation 3)
160M + 240A = 1980 (equation 4)
Now, subtract equation 3 from equation 4 to eliminate M:
120A = 570
Solving for A gives A = 570 / 120 = 4.75 miles.
Now, substitute A = 4.75 into equation 1:
16M + 12*4.75 = 141
16M + 57 = 141
16M = 141 - 57 = 84
Solving for M gives M = 84 / 16 = 5.25 miles.
So, the distance of the morning route is 5.25 miles. The answer is C. 5.25 mi.
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