Two trains, one starting in Calgary and the other in Edmonton, travel towards one another. The Edmonton train travels at 120 km/h toward Calgary, while the Calgary train travels at 140 km/h towards Edmonton. If the trains are 285 km apart, how far from Calgary will the trains pass each other?
At the point where they pass, the total distance traveled(Dc+De) = 285 km,
140T + 120T = 285,
T = 1.1 hours at the point where they pass,
Dc = 140*T = 140*1.1 = 153.5 km = Distance from Calgary.
another perspective;
The relative speed of the calgary departing train is 260km/hr
the distance they both combined travel is 285km
time to meet: 285/260 hr= 57/52 hr
how far from Calgary? 140km/hr * 57/52 hr = ....
On Reiny's response, there is a typo, which affects the cacluations. the 160 should be 120. check that.
To find out how far from Calgary the trains will pass each other, first, we need to determine how long it will take for them to meet.
Let's call the distance from Calgary to the meeting point "x". The distance from the meeting point to Edmonton will then be (285 - x), as the total distance between the two cities is 285 km.
Now, we can use the formula: time = distance / speed.
For the train coming from Edmonton, the time it takes to reach the meeting point will be x km divided by its speed of 120 km/h, so the time is x / 120.
For the train coming from Calgary, the time it takes to reach the meeting point will be (285 - x) km divided by its speed of 140 km/h. So, the time is (285 - x) / 140.
Since both trains are starting at the same time, these two times will be equal, and we can set up an equation:
x / 120 = (285 - x) / 140
Now, we can solve the equation to find the value of x.
First, let's get rid of the denominators by cross-multiplying:
x * 140 = (285 - x) * 120
Expanding the equation:
140x = 34200 - 120x
Adding 120x to both sides:
140x + 120x = 34200
Combining like terms:
260x = 34200
Now, divide both sides by 260:
x = 34200 / 260
x ≈ 131.54
So, the trains will pass each other approximately 131.54 km from Calgary.
I will assume that the trains are 285 km apart, (Google map says it is 300 km)
so after a time of t hours, the distance between them is
285 - 140t - 160t = 285 - 300t
we want that to be zero,
285 - 300t = 0
t = 19/20 hrs.
distance from Calgary = (140)(19/20) km = ...