Three towns A, B, and C lie on a straight road in that order.The distance from
B to C is 6 miles more than twice the distance from A to B.The distance from
A to C is 2 miles more than four times the distance from A to B.What is the
distance from A to B?
To solve this problem, we can start by assigning variables. Let's say the distance from A to B is x miles.
According to the information given, the distance from B to C is 6 miles more than twice the distance from A to B. So, the distance from B to C can be expressed as 2x + 6.
Similarly, the distance from A to C is 2 miles more than four times the distance from A to B. Therefore, the distance from A to C can be expressed as 4x + 2.
From the information given, we know that the three towns lie on a straight road in that order. So, the total distance from A to C would be equal to the sum of the distances from A to B and from B to C.
Therefore, we can set up the following equation: (A to B distance) + (B to C distance) = (A to C distance)
Substituting the expressions we derived earlier:
x + (2x + 6) = (4x + 2)
Now, we can solve the equation to find the value of x, which represents the distance from A to B.
Combining like terms:
x + 2x + 6 = 4x + 2
3x + 6 = 4x + 2
Subtracting 3x from both sides:
6 = x + 2
Subtracting 2 from both sides:
4 = x
So, the distance from A to B is 4 miles.