Laura takes very good care of her vehicles. She owns a blue van and a red truck. Although she bought them both new, she has owned the truck for 17 years longer than she has owned the van. If the sum of the ages of the vehicles is 41 years, how old is the van and how old is the truck?
v + (v+17) = 41
v = 12
so, truck = v+17 = 29
Let's assume the age of the van is represented by V years, and the age of the truck is represented by T years.
Given that Laura has owned the truck for 17 years longer than the van, we can represent this as:
T = V + 17
We also know that the sum of the ages of the vehicles is 41 years, so we can write this as an equation:
V + T = 41
Substituting the first equation into the second equation, we get:
V + (V + 17) = 41
Combining like terms, we have:
2V + 17 = 41
Subtracting 17 from both sides of the equation, we get:
2V = 24
Dividing both sides of the equation by 2, we find:
V = 12
Substituting the value of V back into the first equation, we get:
T = 12 + 17
T = 29
Therefore, the van is 12 years old, and the truck is 29 years old.
To solve this problem, we can set up a system of equations. Let's say the age of the van is represented by "V" and the age of the truck is represented by "T".
We are given two pieces of information:
- Laura has owned the truck for 17 years longer than the van.
- The sum of the ages of the vehicles is 41 years.
Based on this, we can write the following equations:
Equation 1: T = V + 17 (The age of the truck is 17 years longer than the van.)
Equation 2: T + V = 41 (The sum of the ages of the vehicles is 41 years.)
Now, we can solve this system of equations to find the values of T and V.
Substituting Equation 1 into Equation 2, we get:
(V + 17) + V = 41
2V + 17 = 41
2V = 41 - 17
2V = 24
V = 24/2
V = 12
Now, we can substitute the value of V into Equation 1 to find T:
T = 12 + 17
T = 29
Therefore, the van is 12 years old and the truck is 29 years old.