SOLUTION: A train leaves San Diego at 1:00PM. A second train leaves the same city in the same direction at 4:00PM. The second train travels 78mph faster than the first. If the second train o

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A train leaves San Diego at 1:00PM. A second train leaves the same city in the same direction at 4:00PM. The second train travels 78mph faster than the first. If the second train o      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1065085: A train leaves San Diego at 1:00PM. A second train leaves the same city in the same direction at 4:00PM. The second train travels 78mph faster than the first. If the second train overtakes the first at 6:00PM, what is the speed of each of the two trains?
Answer by ikleyn(53763) About Me  (Show Source):
You can put this solution on YOUR website!
.
A train leaves San Diego at 1:00PM. A second train leaves the same city in the same direction at 4:00PM.
The second train travels 78mph faster than the first. If the second train overtakes the first at 6:00PM,
what is the speed of each of the two trains?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let "v" be the speed of the first train (in mph);
then the speed of the second train is (v+78) mph, according to the condition.


Now, the distance traveled by the first train till the overtaking moment was 5v miles, where 5 is/are 5 hours from 1:00 pm till 6:00 pm.

The distance traveled by the second train till the overtaking moment was 2*(v+78) miles, where 2 is/are 2 hours from 4:00 pm till 6:00 pm.


The distance is the same, which gives you an equality

5v = 2(v+78).


Simplify and solve for "v":

5v = 2v + 156  ---->  3v = 156  ---->  v = 156%2F3 = 52.


Answer. The speed of the first train was 52 mph. The speed of the second train was 52 + 78 = 130 mph.

Solved.