Question 1142773: Train A travels 10km/h faster than Train B. These trains travel from area 1 to area 2 which are 100km apart. Train B travels 30 minutes longer than train A to cover the same distance. What is the speed of train B?
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461)   (Show Source):
Answer by ikleyn(52908)  (Show Source):
You can put this solution on YOUR website! .
When students solve such problems, the major difficulty is to setup a governing equation.
I will show you a standard and straightforward way to do it.
Let r be the rate of train B, in kilometers per hour (the unknown value under the question).
Then the rate of the train A is (r+10) km/h, according to the condition.
Train's B traveling time is  hours.
Train's A traveling time is  hours.
The difference of traveling times is  of an hour, according to the condition.
It gives you this "time" equation
- = hours. <<<---=== Every fraction on the left side is the traveling time . . .
At this point, the setup is just completed (!)
To solve the equation, multiply both sides by 2*r*(r+10). You will get
200*(r+10) - 200*r = r*(r+10)
2000 = r^2 + 10r
r^2 + 10r - 2000 = 0
(r+50)*(r-40) = 0
The two roots of the equation are r = -50 and r = 40, but only positive r = 40 km/h makes sense and is the solution to the problem.
ANSWER. The rate of train B is 40 kilometers per hour.
CHECK. Travel time for train A is  =  = 2 hours;
Travel time for train B is  =  hours, which is 30 minutes longer than that of train A. ! Correct !
Solved
Using "time" equation is the STANDARD way to solve such problems.
From this solution, learn on how to write, how to use and how to solve a "time" equation.
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To see many other similar solved problems, look into the lessons
- Had a car move faster it would arrive sooner
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- Time equation: HOW TO use, HOW TO write and HOW TO solve it
in this site.
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