Please help! Simple Math Problem!?

Aussie: Please help! Simple Math Problem!?
two commuter trains carry passengers between two cities, one travelling east, and the other west, on different tracks. Their respective stations are 150 miles apart. both trains leave at the same time, one travelling at an average speed of 55 miles per hour and the other at an average speed of 65 miles per hour. let t represent the time until the trains pass each other

a)write an equation using t that describes the distances travelled

b)how long after departing will the train pass each other.

I don’t understand part a).. I can work out b) but I really don’t know a)! How can you do a) without the info gained in b)?

As t is the time until they pass it will become negative after they pass. Does my teacher mean the distance train A and train B travel added together? If so I have NO idea how to relate this to t!

Please help! Quick points!

Answers and Views:

Answer by Gerry
Two trains which depart their respective stations at the same instant, traveling to each other’s station, will pass each other at the same instant. So you want to find the distance each has traveled until they pass:

65t = distance covered by train A traveling at 65 miles per hour.
55t = distance covered by train B traveling at 55 miles per hour.

Since they are each traveling along until they pass each other, you have to add these two distances, set them equal to 150, and solve for t:

A——————65t miles————–><---------55t miles------------B |<---------------------------------- (150 miles) ------------------------------>|

65t + 55t= 150

120t = 150

t = 1.25 hrs

b) The trains will pass each other 1 hour 15 minutes after leaving their respective stations.

To solve for the distance, simply set t = 1.25:

65t = 65(1.25) = 81.25 miles

55t = 55(1.25) = 68.75 miles

a) So in one-and-a-quarter hours train A travels 81-1/4 miles and train B travels 68-3/4 miles.