Two trains, one starting in Calgary and the other in Edmonton, travel toward one another. The Edmonton train travels at 120 km/h toward Calgary, while the Calgary train travels at 140 km/h toward Edmonton. If the trains begin at the same time and Edmonton and Calgary are 285 km apart, how far from Calgary will the trains pass each other? (153 km)
Well, well, well, it seems like these trains are in a hurry to meet each other! Let's do some math and find out where the magical meeting point is.
The Edmonton train is zooming towards Calgary at a speed of 120 km/h, while the Calgary train is not far behind, cruising at 140 km/h. Now, since both trains started at the same time, we have to take into account their combined speed.
The total speed at which the trains are approaching each other is the sum of their speeds: 120 km/h + 140 km/h = 260 km/h.
We're told that Edmonton and Calgary are 285 km apart, so we need to figure out how much time it will take for the trains to meet. We can use the formula time = distance/speed.
Time = 285 km / 260 km/h ≈ 1.096 hours.
Now that we know the time it takes for the trains to meet, we can find the distance from Calgary where they pass each other. We can use the formula distance = speed × time.
Distance = 140 km/h × 1.096 hours = 153.44 km.
Voila! The trains will pass each other approximately 153 km away from Calgary. Safe travels, choo-choo!
To determine the distance from Calgary where the trains will pass each other, we need to consider the relative speed at which the trains are approaching each other.
Since the Edmonton train is traveling towards Calgary at 120 km/h and the Calgary train is traveling towards Edmonton at 140 km/h, the combined speed at which they are approaching each other is the sum of their speeds, which is 120 km/h + 140 km/h = 260 km/h.
To find the time it takes for the trains to meet, we divide the distance between Edmonton and Calgary (285 km) by their combined speed (260 km/h):
Time = Distance / Speed = 285 km / 260 km/h = 1.096 hours
To determine the distance from Calgary where the trains will meet, we need to multiply the time it takes by the speed of the Calgary train since it is moving towards Edmonton:
Distance = Time * Speed = 1.096 hours * 140 km/h ≈ 153 km
Therefore, the trains will pass each other approximately 153 km from Calgary.
To find out how far from Calgary the trains will pass each other, we need to determine how long it will take for them to meet.
Let's say the distance from Calgary to the meeting point is represented by x. Therefore, the distance from the meeting point to Edmonton is (285 - x).
To find the time it will take for each train to reach the meeting point, we can use the formula:
Time = Distance / Speed
For the Edmonton train:
Time1 = (285 - x) / 120
For the Calgary train:
Time2 = x / 140
Since both trains start at the same time, the times for each train must be equal. Therefore, we have the equation:
(285 - x) / 120 = x / 140
To solve for x, we can cross multiply:
140(285 - x) = 120x
Simplifying the equation:
39900 - 140x = 120x
Combining like terms:
39900 = 260x
Dividing both sides by 260:
x = 153
Therefore, the trains will pass each other 153 km away from Calgary.