Bunuel wrote:
Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 49 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?
(A) 105
(B) 120
(C) 140
(D) 147
(E) 168
Kudos for a correct solution.
These type of questions are still my biggest weakness, but I think explaining it help me... Feel free to give me feedback on my method. Please also bear with the fact that I am explaining every single step in my reasoning... Maybe it will help someone one day.
Rate * Distance = TimeWhere \(T =\) time
Car Y driving in Hours & \(D =\) Distance in Miles
Car X: \(35 * (T + \frac{6}{5}) = D\)
Car Y: \(49 * T = D\)
---> \(35(T + \frac{6}{5}) = 49T\)
---> \(35T + \frac{210}{5} = 49T\)
---> \(35T + 42 = 49T\)
---> \(14T = 42\)
---> \(T = \frac{42}{14} = 3\)
So we know that They both drove the same distance after
Car Y had been driving for 3 hours. The question asks how far
Car X had driven after this amount of time ---> \(35 * 3 = 105\) miles
Answer = A