a train left podunk and traveled west 70 km/h. two hours later, another train left podunk and traveled east at 90km/h. how many hours had the first train traveled when they were 1420 km apart?
After t hours since the second train left the station,
the first train went 70t + 140
the second train 90t
so solve 70t + 140 + 90t = 1420
(I got t=8, confirm this please)
Well, let's put on our conductor hats and calculate this! If the first train is traveling west at 70 km/h for x hours, it would have traveled a distance of 70x km. The second train, traveling east at 90 km/h, would have traveled for (x - 2) hours. Now we can set up an equation:
70x + 90(x - 2) = 1420
To solve this equation, we can simplify it:
70x + 90x - 180 = 1420
160x = 1600
x = 10
So, the first train would have traveled for 10 hours when they were 1420 km apart. Just enough time for a few onboard comedy shows, I suppose!
Let's calculate the time it took for the second train to catch up to the first train.
First, we need to determine the time it took for the second train to catch up to the first train after it left.
The second train is traveling 90 km/h, which is 20 km/h faster than the first train's speed. Therefore, it will catch up to the first train at a rate of 20 km/h.
To find the time it took for the second train to catch up, we can use the formula:
Time = Distance / Speed
The distance covered by the first train during this time is the speed multiplied by the time:
Distance = Speed * Time
Let's denote the time taken by the second train as "t" hours.
Distance covered by the first train during this time = 70 km/h * t hours = 70t km
Now, the total distance between the trains when they were 1420 km apart can be expressed as follows:
Distance = Distance covered by the first train + Distance covered by the second train
1420 km = 70t km + (70t km + 2 hours * 90 km/h)
1420 km = 70t km + 70t km + 180 km
1420 km = 140t km + 180 km
Rearranging the equation:
140t km = 1420 km - 180 km
140t km = 1240 km
Dividing both sides by 140:
t = 1240 km / 140 km/h
t ≈ 8.86 hours
Therefore, it took approximately 8.86 hours for the second train to catch up to the first train.
Since the second train left Podunk two hours after the first train, we need to add those two hours to find out how many hours the first train traveled.
Total hours the first train traveled = 8.86 hours + 2 hours
Total hours the first train traveled ≈ 10.86 hours
The first train had traveled approximately 10.86 hours when the trains were 1420 km apart.
To find the number of hours the first train had traveled when they were 1420 km apart, we need to figure out the time it took for the second train to cover the same distance.
Let's start by calculating the time it took for the second train to reach the 1420 km mark.
The first train traveled at a speed of 70 km/h, and it left two hours earlier than the second train. Therefore, the first train traveled for (2 + t) hours.
The second train traveled at a speed of 90 km/h, and it traveled for t hours.
We can use the formula distance = speed x time to calculate the distance each train traveled.
For the first train: 70 km/h * (2 + t) hours
For the second train: 90 km/h * t hours
Since the total distance between the two trains is given as 1420 km, we can write the equation:
70 km/h * (2 + t) hours + 90 km/h * t hours = 1420 km
Now we can solve this equation to find the value of t, which represents the time it took for the second train to cover 1420 km.
70 km/h * (2 + t) + 90 km/h * t = 1420 km
140 km + 70 km/h * t + 90 km/h * t = 1420 km
140 km + 160 km/h * t = 1420 km
160 km/h * t = 1280 km
Dividing both sides of the equation by 160 km/h:
t = 1280 km / 160 km/h
t = 8 hours
So, the second train took 8 hours to cover the distance of 1420 km.
To determine the time the first train had traveled when they were 1420 km apart, we add the 2 hours it left earlier to this time:
Time of the first train = 2 hours + 8 hours = 10 hours
Therefore, the first train had traveled for 10 hours when they were 1420 km apart.