Problema Solution

Train 12 leaves downtown and travels at an average speed of 45mph towards the north side station which is 58.8 miles away

12 minutes later train 7 leaves the north side station and travels at an average speed 45 mph towards downtown.

At the moment the two trains pass each other, how far (in miles) is the 12 train from downtown and how long (in minutes) has the 12 train been traveling?

If the answer is not an integer, enter I as an exact decimal.

12 train is ________ miles from downtown and been traveling for _________ minutes.

Answer provided by our tutors

 Converting from mins to hrs (since avg speed is mile/hr): 12mins = 12/60 = 0.2 hr

After 12 mins, train 12 traveled: 0.2hr * 45mph = 9 miles

So, train 12 is 58.8 - 9 = 49.8 miles away from north side station

When two trains pass each others, the total distance of both trains will be 49.8 miles

(since two trains travel at same avg speed, and travel at the same time since train 7 leaves the north side)

=> v12 * t12 + v7 * t7  = 2 (v12 * t12) = 49.8 = 2*(45mph *t12 ) = 49.8

 solve for t12 -> t12 = 0.553333 hr = 0.553hr * 60mins = 33.18 mins

Train 12 has been traveling for 33.18 + 12 =45.18 mins

Train 12 is 58.8 - s7  = 58.8 - (v7 * t7) = 58.8 - (45*0.553)  = 33.915  miles from downtown

     or  = (0.553 + 0.2) * 45 =  v12 * t12  (note: there will be a little error since I round up 0.553333 to 0.553 but it doesn't matter anw)