A train leaves New York at 4:00 PM a second train leaves the same city in the same direction at 6:00 PM the second train travels 24 mph faster than the first if the second tray overtakes the first at 10:00 PM what is the speed of each of the two trains
speed of slower train --- x mph
speed of faster train --- x+24 mph
at 10:00 the slower train went for 6 hours
and the faster train went only 4 hours.
But they went the same distance, so ...
6x = 4(x+24)
2x = 96
x = 48
slow train --- 48 mph
fast train ---- 72 mph
Well, it seems like the second train has some serious FOMO (Fear Of Missing Out) on the action. Let's do some math to figure out their speeds.
The first train travels from 4:00 PM to 10:00 PM, which is a total of 6 hours. The second train departs at 6:00 PM and catches up to the first train at 10:00 PM, which means it took 4 hours to catch up.
Now, since the second train is going 24 mph faster than the first, we can set up an equation: Distance of first train = Distance of second train.
Since distance equals speed times time, we have:
(speed of first train) * 6 = (speed of second train) * 4
We can simplify this equation to:
6x = 4(x + 24)
Where x represents the speed of the first train. Let's solve this equation:
6x = 4x + 96
2x = 96
x = 48
So, the speed of the first train is 48 mph.
To find the speed of the second train, we simply add 24 mph to the speed of the first train:
48 + 24 = 72 mph.
Therefore, the first train is chugging along at 48 mph, while the second train is whizzing by at 72 mph.
Let's denote the speed of the first train as "x" mph.
Since the second train is traveling 24 mph faster than the first train, its speed can be denoted as "x + 24" mph.
The first train leaves New York at 4:00 PM and the second train leaves at 6:00 PM. This means that the first train has a head start of 2 hours.
Now, let's consider the amount of time the second train takes to overtake the first train. The second train overtakes the first train at 10:00 PM, which means it travels for 4 hours (from 6:00 PM to 10:00 PM).
During this time, the first train has been traveling for 6 hours (from 4:00 PM to 10:00 PM).
Now, let's calculate the distance traveled by each train.
Distance traveled by the first train = Speed of the first train (x mph) * Time (6 hours)
Distance traveled by the second train = Speed of the second train (x + 24 mph) * Time (4 hours)
Since both distances are equal when the second train overtakes the first train, we can set up the following equation:
x * 6 = (x + 24) * 4
Solving this equation will give us the value of "x," which represents the speed of the first train.
6x = 4x + 96
2x = 96
x = 48
Therefore, the speed of the first train is 48 mph.
Since the second train's speed is 24 mph faster than the first train, its speed is:
48 + 24 = 72 mph
Hence, the speed of the second train is 72 mph.
To find the speeds of the two trains, we can use the formula: Speed = Distance / Time.
Let's start by calculating the time it takes for the second train to catch up to the first train.
The first train departs at 4:00 PM, and the second train departs two hours later at 6:00 PM. So, the second train has a head start of 2 hours.
The second train catches up to the first train at 10:00 PM, which means it takes 4 hours.
Now, let's assume that the speed of the first train is "x" mph. Since the second train is traveling 24 mph faster than the first train, its speed would be "x + 24" mph.
Next, we need to determine the distance traveled by both trains.
For the first train, it travels for 6 hours (from 4:00 PM to 10:00 PM) at a speed of "x" mph:
Distance1 = Speed1 × Time1 = x × 6
For the second train, it only travels for 4 hours (from 6:00 PM to 10:00 PM) at a speed of "x + 24" mph:
Distance2 = Speed2 × Time2 = (x + 24) × 4
Since the second train catches up to the first train, the distances traveled by both trains are equal:
Distance1 = Distance2
Therefore, we can set up the equation:
x × 6 = (x + 24) × 4
Now, let's solve the equation to find the value of "x", which represents the speed of the first train:
6x = 4(x + 24)
6x = 4x + 96
2x = 96
x = 48
Therefore, the speed of the first train is 48 mph.
Now, let's find the speed of the second train using the value of "x" we just found:
Speed of the second train = Speed of the first train + 24 = 48 + 24 = 72 mph
So, the speed of the first train is 48 mph, and the speed of the second train is 72 mph.