SOLUTION: it takes a freight train 3 hours more to travel 200 miles than it takes an express train to travel 120 miles. the express train is 20 mph faster than the freight train. find the ra
Algebra.Com
Question 347212: it takes a freight train 3 hours more to travel 200 miles than it takes an express train to travel 120 miles. the express train is 20 mph faster than the freight train. find the rate of both trains
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
it takes a freight train 3 hours more to travel 200 miles than it takes an
express train to travel 120 miles.
the express train is 20 mph faster than the freight train.
find the rate of both trains
:
Let s = speed of the freight
then
(s+20) = speed of the express
:
Write a time equation, time = dist/speed
:
Freight time - express time = 3 hrs
- = 3
:
multiply by s(s+20), results:
200(s+20) - 120s = 3s(s+20)
:
200s + 4000 - 120s = 3s^2 + 60s
:
80s + 4000 = 3s^2 + 60s
:
0 = 3s^2 + 60s - 80s - 4000
A quadratic equation
3s^2 - 20s - 4000 = 0
Factors to:
(3x + 100)(s - 40) = 0
the positive solution is what we want here:
s = 40 mph is the freight
then
40 + 20 = 60 mph is the express
:
:
Check solution by finding the travel time of each
200/40 = 5 hr
120/60 = 2 hr
-------------
differs: 3 hr
RELATED QUESTIONS
It takes a freight train 3 hours more to travel 200 miles than it takes an express train... (answered by scott8148)
It takes a freight train 3 hours more to travel 280 miles than it takes an express train... (answered by mananth)
Please help me solve this word problem: It takes a freight train 2 hours more to travel... (answered by sudhanshu_kmr)
It takes a freight train 2 hours longer to travel 200 miles than it takes an express... (answered by stanbon)
It takes a freight train 2 hrs longer to travel 300 miles than it takes an express train... (answered by Paul,stanbon)
A freight train takes 2 hours longer to travel 300 miles than an express train to travel... (answered by checkley77)
An express train travels 600 miles in the same amount of time it takes a freight train to (answered by Mathtut)
an express train traveled 600 miles in the same amount of time it takes a freight train... (answered by hamsanash1981@gmail.com)
Need help with setting up formula for: An express train is 19mph faster than a freight... (answered by oscargut)