How do you do this math word problem?

Question

A train leaves New York for Boston, 200 miles away, at 3:00 P.M. and averages 65 mph. Another train leaves Boston for New York on an adjacent set of tracks at 5:00 P.M. and averages 70 mph. At what time will the trains meet?

Answer 1

First off ask yourself where are both trains at 5:00 P.M?

The New York train is 70 miles from Boston.

Now the New York is going to travel another x miles before they meet and it will take that train (since v=x/t), t = x/65 hours to get there.

The Boston train is going to travel (70 - x) miles when they meet. It will take that train t=(70-x)/70 hours to get there.

So two equations two unknowns.
t = x/65
t = (70-x)/70

solve for t, it will be in hours, multply by 60 to get minutes. (it will be greater than 30 minutes)

Time will be the minutes found above + 5:00 p.m, so something after 5:30

Answer 2

The first train will be 130 miles closer to the second train when the second train leaves at 5:00 PM. They will be 70 miles apart at 5:00 pm.They are traveling at a combined speed of 135 miles per hour,or 2.25 miles per minute it will take 31.1 minutes ( 70 divided by 2.25 ) for the trains to pass each other.They will pass each other at 5:31 and 6 seconds PM

Answer 3

Here is how I would do it.

Let t be the amount of time in hours, after 5pm, that the trains meet.
At 5pm, the NY train will have already travelled 65*2=130 miles.
At this point, the trains are 70 miles apart.
After t hours, the NY train will have travelled 65t more miles.
After t hours, the Boston train will have travelled 70t miles.
65t + 70t = 70 miles
135t = 70
t = 0.5185 hours after 5pm, which is about 5:31pm.

Not sure if I did that right, so let me check my work.

NY train: (2.5185 hr) * (65 mph) = 163.7 miles
Bo. train: (0.5185 hr) * (70 mph) = 36.3 miles
163.7 mi + 36.3 mi = 200 miles.
Looks good to me.

Answer 4

4:20

Answer 5

ye use the system of linear equations in two vars

Answer 6

They wont meet...they will pass each other.
:)