Answer:
A is 29 miles and B is 18 miles
Explanation:
Set up 2 equations involving A and B and solve simultaneously, that is
5A + 2B = 181 → (1)
2A + 3B = 112 → (2)
Multiply (1) by 3 and (2) by - 2 to eliminate B
15A + 6B = 543 → (3)
- 4A - 6B = - 224 → (4)
Add (3) and (4) term by term to eliminate B
(15A - 4A) + (6B - 6B) = 543 - 224, that is
11A = 319 ( divide both sides by 11 )
A = 29
Substitute A = 29 into either of the 2 equations and solve for B
Substituting into (1)
5(29) + 2B = 181
145 + 2B = 181 ( subtract 145 from both sides )
2B = 36 ( divide both sides by 2 )
B = 18
Thus
Route A is 29 miles long and Route B is 18 miles long.