A freight train leaves a station traveling at 32 km/h. Two hours later, a passenger train leaves
the same station traveling in the same direction at 52 km/h. How long does it takes the passenger
train to catch up to the freight train?
32 (t + 2)= d
52 t = d
so
32 t + 64 = 52 t
20 t = 64
t = 3.2 hours and 12 minutes
==========================
check
32 * 5.2 = 166.4
52 * 3.2 = 166.4
good
the freight train has a 64 km head start ... 32 kph * 2 h
the passenger train closes the distance at 20 kph ... 52 kph - 32 kph
64 / 20 = ?
To find out how long it takes for the passenger train to catch up to the freight train, we can set up an equation based on their respective speeds.
Let's assume it takes "t" hours for the passenger train to catch up to the freight train.
During the 2-hour head start that the freight train has, it will travel a distance of:
Distance freight train travels = Speed of freight train * Time
Distance freight train travels = 32 km/h * 2 hours = 64 km
Now, for the passenger train to catch up to the freight train, its distance traveled must be equal to the distance traveled by the freight train:
Distance passenger train travels = Distance freight train travels
Speed of passenger train * Time = 64 km
Since the speed of the passenger train is 52 km/h, we can write the equation as:
52 km/h * t hours = 64 km
To find the value of "t", we can solve this equation:
t = 64 km / 52 km/h
Using basic unit cancellation, we can simplify this:
t = 1.23 hours
Therefore, it takes approximately 1.23 hours (or 1 hour and 14 minutes) for the passenger train to catch up to the freight train.
Please note that the answer has been rounded to two decimal places.
To find out how long it takes for the passenger train to catch up to the freight train, we need to find the time difference between the two trains. Let's break down the problem and find a solution.
1. Determine the distance traveled by the freight train in the two-hour time period:
Distance = Speed × Time
Distance = 32 km/h × 2 hours = 64 km
2. Now, let's set up a scenario where the passenger train catches up to the freight train at some point. At that moment, both trains will have traveled the same distance. Let's denote this distance as "D".
3. Since the passenger train leaves two hours later, we can use the equation: Distance = Speed × Time for the passenger train. The time traveled by the passenger train (T) can be represented as:
Distance = 52 km/h × T
4. Since both trains have traveled the same distance when the passenger train catches up, we can set up the equation: D = 64 km + 52 km/h × T
5. Solving for T:
64 km + 52 km/h × T = 52 km/h × T
64 km = 52 km/h × T - 52 km/h × T
64 km = 0 km/h × T
T = 0 km/h / 52 km/h
6. Simplifying the equation:
T = 0 hours
This implies that the passenger train catches up to the freight train immediately after it starts moving, i.e., it takes 0 hours for the passenger train to catch up to the freight train.