First, it has been a while since I've had to do any formalized math problems, and my skills are a bit rusty. I was recently presented with a story problem, and my initial impression is that it is impossible to solve with the given information (perhaps some part was left out accidentally when I was asked?). I am no expert, however, so I'd like to see if anyone more knowledgeable than me can either confirm my suspicion, or explain a bit how to get an answer. The question is as follows:
"You have two cars starting from two different points and traveling in straight lines such that their paths will cross at some point. They each travel an equal total distance from start to finish, and after their paths intersect, it takes one car 1 hour and the other car 9 hours to reach their respective destinations. How much faster is the one car compared to the other?"
My thought process is this, but please correct me if I am wrong about anything:
-> Distance = rate * time
-> We know each car travels the same distance overall, and we know a part of the total time taken. So if Ra and Rb are the cars' respective rates, then given the distance formula and what we know:
Ra(x + 1) = Rb(y + 9) [where x and y are the unknown portions of time before the intersection point of the cars]
-> Given the problem, I suppose we also know that the cars have different rates, such that:
Ra = zRb [where z essentially represents the answer to the question]
-> Now we could obviously substitute one of the rate variables to get something like:
zRb(x + 1) = Rb(y + 9)
-> But then we still essentially have 4 different unknowns to deal with. And even though we don't strictly speaking need values for Ra or Rb (as we are only technically interested in the multiple z for the answer) and can simply:
z = (y + 9)/(x + 1)
-> That still leaves x, y, and z unknown, and I just don't see a way to obtain a simple numerical value for z here given what we have.
At any rate (pun sort of intended), any thoughts or help anyone has is greatly appreciated so I can stop chasing this one around in my head. Thanks in advance!
"You have two cars starting from two different points and traveling in straight lines such that their paths will cross at some point. They each travel an equal total distance from start to finish, and after their paths intersect, it takes one car 1 hour and the other car 9 hours to reach their respective destinations. How much faster is the one car compared to the other?"
My thought process is this, but please correct me if I am wrong about anything:
-> Distance = rate * time
-> We know each car travels the same distance overall, and we know a part of the total time taken. So if Ra and Rb are the cars' respective rates, then given the distance formula and what we know:
Ra(x + 1) = Rb(y + 9) [where x and y are the unknown portions of time before the intersection point of the cars]
-> Given the problem, I suppose we also know that the cars have different rates, such that:
Ra = zRb [where z essentially represents the answer to the question]
-> Now we could obviously substitute one of the rate variables to get something like:
zRb(x + 1) = Rb(y + 9)
-> But then we still essentially have 4 different unknowns to deal with. And even though we don't strictly speaking need values for Ra or Rb (as we are only technically interested in the multiple z for the answer) and can simply:
z = (y + 9)/(x + 1)
-> That still leaves x, y, and z unknown, and I just don't see a way to obtain a simple numerical value for z here given what we have.
At any rate (pun sort of intended), any thoughts or help anyone has is greatly appreciated so I can stop chasing this one around in my head. Thanks in advance!
