Question 1135240: A train leaves Orlando at 1:00 pm. A second train leaves the same city in the same direction at 4:00 pm. The second train travels 30mph faster than the first. If the second train overtakes the first at 10:00 pm, what is the speed of each of the two trains?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52792)   (Show Source):
You can put this solution on YOUR website! .
Let x be the speed of the first train, in miles per hour (mph).
Then the speed of the second train is (x+30) mph, according to the condition.
From 1 pm to 10 pm, the first train moved 9 hours and covered the distance of 9*x miles (recall the formula Distance = Time*Speed (!) )
From 4 pm to 10 pm, the second train moved 6 hours and covered the distance of 6*(x + 30) miles (same "distance" formula).
The distance is the same in both cases - it gives you an equation
9x = 6*(x+30).
Simplify and solve it for x:
9x = 6x + 180
9x - 6x = 180
3x = 180 ==============> x =  = 60.
Answer. The first train' speed was 60 mph; the second train' speed was 60+30 = 90 mph.
CHECK. 9*60 = 540 miles = 6*90. ! Correct !
The solution is just completed.
----------------
See introductory lessons on Travel and Distance problems
- Travel and Distance problems
- Travel and Distance problems for two bodies moving in opposite directions
- Travel and Distance problems for two bodies moving in the same direction (catching up)
in this site.
They are written specially for you.
You will find the solutions of many similar problems there.
Read them and learn once and for all from these lessons on how to solve simple Travel and Distance problems.
Become an expert in this area.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The solution from tutor @ikleyn uses probably the most common algebraic approach to the problem.
Here is a different method that I like to use on problems like this.
(1) The first train traveled from 1pm until 10pm, 9 hours; the second traveled from 4pm until 10pm, 6 hours.
(2) The distances are the same, and the ratio of the times is 3:2. That means the ratio of speeds is 2:3.
(3) If the ratio of the speeds is 2:3 and the difference in the speeds is 30mph, then the two speeds are 60mph and 90mph.
|
|
|
