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
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