2) 200 km
Hi, i was just wondering if anyone could help me out with these two math questions from my homework.
question 1.) solve the system of equations
question 2.)a tain leaves toronto for montreal at the same time as another train leaves montreal for toronto. the cities are 500km apart. The trains pass each other 2 hours later. the train leaving montreal is travelling 50km/h faster than the one leaving from toronto. at what distance away from toronto do the trains pass each other?
1.) One method we may use is elimination. I would begin by taking the first two equations:
Notice if we add the equations together, we will eliminate the z:
Next, we could take -5 times the first equation and add it to the third to also eliminate z: Then you will have a 2X2 system in x and y, which you may solve, then you will be able to find z from any of you original equations.
2.) Let train 1 be the train that departed Toronto, and train 2 be the train that departed Montreal. We will subscript all variables accordingly. We are being asked to find
After traveling for 2 hours, the trains meet, so we know the sum of their traveled distances is 500 km:
We are also told:
The relationship between distance, speed and time is , so we may state:
Using the above information, you can find the quantity in question.
Another approach . . .
2) A train leaves Toronto for Montreal at the same time as another train leaves Montreal for Toronto.
The cities are 500km apart. .The trains pass each other 2 hours later.
The train leaving Montreal is travelling 50km/hr faster than the one leaving from Toronto.
At what distance away from Toronto do the trains pass each other?
Let = speed of the train leaving Toronto.
Then = speed of the train leaving Montreal.
In 2 hours, they meet atCode:: 2v : 2(v+50) : *-------->*<--------------* T X M : - - - - - 500 - - - - - :
The train from Toronto has traveled km.
The train from Montreal has traveled km.
Together, they covered 500 km: .
. . Hence: . km/hr.
Therefore, is: km from Toronto.