A freight train leaves Kansas City and travels due west. A passenger train departs at exactly the same time on a parallel track and travels due east at a speed that is twice the speed of the freight train. After seven hours the trains are 945 miles apart. How fast is each trian traveling??
How do I go about solving this?? I tried to read one line at a time, but it is to overwhelming.
Thanks
2007-09-14 07:22:01 · 13 answers · asked by k_artiaco 1 in Education & Reference ➔ Homework Help
Speed of freight train = x
speed of passenger train = 2x
distance = velocity * time
d= 945, t = 7 hours
d = vt
945 = (2x+x)(7)
945 = (3x)(7)
3x = 135
x=45
so the freight train is traveling at 45 mph, and twice that is 90 mph, which is the speed of the passenger train.
2007-09-14 07:33:38 · answer #1 · answered by remowlms 7 · 5⤊ 2⤋
You just need to find the mathematical equivalent of the words -- it's kind of like translating a foreign language. Here's what we know:
The trains start at the same point at the same time.
One is traveling twice the speed of the other.
They travel for seven hours.
They end up 945 miles apart.
1) You need to determine how fast each train is traveling; so your unknowns will be the speeds of the trains.
2) Let x = the speed of the first train
Let 2x = the speed of the second train (because we know it's traveling twice as fast).
3) They've been traveling seven hours, so we know the first train has traveled 7x and the second train has traveled 7(2x).
4) 7x + 7(2x) = 945 (because we know they are 945 miles apart).
5) Simplify:
7x + 14x = 945
21x = 945
x = 945/21 = 45
The first train is traveling 45 mph, and the second is traveling 90 mph.
Hope that helped.
2007-09-14 14:35:12 · answer #2 · answered by Kathryn 6 · 3⤊ 0⤋
Hello
Word problems are always difficult for people. The first thing you should do to simplify is draw a picture. Most people will get some idea from visualization. Then identify all the knowns and unknowns.
The two trains total distance is 945 miles. We know that they have traveled for 7 hours. We know that x is the speed of the slower train and 2x is the speed of the faster train.
7(2x+x)=945
14x+7x=945
21x=945
x=45
2x=90
Good Luck! I know you can do it!!!
2007-09-15 11:26:11 · answer #3 · answered by Marge S 2 · 0⤊ 0⤋
Focus on one train at a time. First, look at the train traveling west. In 7 hours, that train is how many miles from the starting point? That is not known.
Next, look at the train traveling east. In 7 hours, how many miles is it away from the starting point? That is also unknown.
Next, I like to draw a picture of the problem. The trains started at the same place, at the same time. The east train traveled 2x faster than the west train. In 7 hours, they were 945 miles apart.
Last, it is now your turn to come up with a math equation to help you solve for the answer.
2007-09-14 14:39:13 · answer #4 · answered by Andrew G 2 · 0⤊ 0⤋
The trick is to get rid of the extra useless details.1st figure out how much of the 945 miles had each train gone.Since 1 is only going 1/2 the speed of the other you can figure that 1 only traveled 1/3 the distance.So train1 went 315 miles while train 2 went 630miles.Then divide each by 7 to figure how many miles per hour each went. Train 1 is going 45 mph while train 2 went 90mph. I think that this is correct. If not then I'm very sorry. I am usually pretty good with word problems.
2007-09-14 19:52:26 · answer #5 · answered by Enigma 2 · 0⤊ 1⤋
Think about proportions. One train travels twice as fast as the other so travels twice as far in the same time. So if you think of the distance as x then you have
2x + x = 945
So 3x = 045
So x = 945/3 = 315
Thus the slower train travels at 315/7 mph = 45 mph
The other is twice as fast = 90 mph
2007-09-14 14:31:39 · answer #6 · answered by quatt47 7 · 4⤊ 1⤋
Let's see:
If the slower train's rate of speed is x, that means the other train's speed is 2x, so if they go for 7 hours and end up 945 miles apart:
7x + 7(2x) = 945
Multiply it out:
7x + 14x = 945
Add the two like terms together:
21x = 945
Divide both sides by 21:
x = 45, so the slower train is traveling at a rate of 45 MPH and the faster train (2x) is traveling at a rate of 90 MPH
2007-09-14 14:31:43 · answer #7 · answered by Anonymous · 7⤊ 1⤋
Draw a picture to help you visualize it. Make sure you draw the distance of B to be twice that of A. You can then split the total distance into three equal parts. How far is each piece? Once you know that, you know the speed of Train A over the seven hour period and can then find the speed per hour for each train.
Train A ...X......Train B
A to B is 945 miles
Sorry, but I won't give you the answer directly.
2007-09-14 14:31:53 · answer #8 · answered by MJ3000 4 · 1⤊ 2⤋
Try rewording it.
They're moving away from each other. One is moving twice as fast as the other.
Their speed is how fast each is moving from Kansas City.
They're moving slow-train-speed X 3 from each other.
Also, simplify it where you can.
After 7 hours, they're 945 miles apart, so -- since you're looking for miles per hour, get how far apart they were after ONE hour?
The speed of the first is 1/3 of that speed.
2007-09-14 17:38:40 · answer #9 · answered by tehabwa 7 · 0⤊ 1⤋
Ok, you need to establish a mathematical relationship between the two velocities.
Veast = 2 Vwest
Also, Veast * 7 + Vwest * 7 = 945
Now you have two equations with two unknowns. Solve.
2007-09-14 14:28:54 · answer #10 · answered by Anonymous · 0⤊ 0⤋