Each week Lance drives two routes, route A and route B.
One week he drives route A five times and route B twice.
He drives a total of 181 miles that week.
The week after, he drives route A twice and route B three times.
He drives a total of 112 miles that week.
Find the length of each route.
Route A = 29
Route B = 18
To find the length of each route, let's assign variables to represent the lengths of route A and route B.
Let's say:
Length of route A = x
Length of route B = y
We can use this information to set up two equations:
Equation 1: 5x + 2y = 181
Equation 2: 2x + 3y = 112
Now, we have a system of two equations with two variables. To solve this system, we can use substitution or elimination method. Let's use the elimination method in this case.
Multiplying equation 1 by 2 and equation 2 by 5 to eliminate the x term, we get:
10x + 4y = 362
10x + 15y = 560
Now, subtract equation 1 from equation 2:
(10x + 15y) - (10x + 4y) = 560 - 362
11y = 198
Dividing both sides of the equation by 11, we find:
y = 18
Now, substitute the value of y back into equation 1 or 2 to solve for x. Let's use equation 1:
5x + 2(18) = 181
5x + 36 = 181
5x = 181 - 36
5x = 145
Dividing both sides of the equation by 5, we find:
x = 29
Therefore, the length of route A is 29 miles, and the length of route B is 18 miles.
Joe mama
length of route A ---- a
length of route B --- b
5a + 2b = 181
2a + 3b = 112
I would use elimination:
1st by 3: ----> 15a + 6b = 543
2nd by 2: --> 4a + 6b = 224
subtract those to get a = ...
sub that back into 2a + 3b = 112 to find b