5) 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?
Its a basic question but i never understood this kind of problem
the distance traveled is the same
distancefirst=32*time
distancesecond=52*(time-2)
set them equal, solve for time.
I think i may have found out the right answer but a little different then you did. Can you check this and tell me if im right pls?
I got 3.2 hours as my answer.
the way i did it was more of drawing it out then eqaution.
when the 2nd train starts the 1st is already 64km away. Every hour after that the 2nd train catches up 20km.
From there i divided 64/20 which is 3.2.
To solve this type of problem, we need to understand the concept of relative speed. Relative speed refers to the speed of an object relative to another object. In this case, we want to find out how long it takes for the passenger train to catch up to the freight train, which means we want to know when the relative distance between them becomes zero.
Here's how you can approach this problem step-by-step:
Step 1: Determine the time difference between the two trains leaving the station.
In this case, we are told that the freight train leaves the station two hours before the passenger train. This means the passenger train has a head start of two hours.
Step 2: Calculate the distance traveled by the freight train during this time.
Since we know the speed of the freight train is 32 km/h, and it travels for two hours, we can use the formula Distance = Speed × Time to calculate the distance traveled:
Distance = 32 km/h × 2 h = 64 km.
Step 3: Set up an equation to represent the situation.
Let t be the time it takes for the passenger train to catch up to the freight train. At that time, the distance traveled by the passenger train will be equal to the distance traveled by the freight train plus the head start distance.
Step 4: Write the equation and solve for t.
Distance traveled by the passenger train = Distance traveled by the freight train + Head start distance
Speed of the passenger train × t = Speed of the freight train × t + Distance of the head start
52 km/h × t = 32 km/h × (t + 2 h) + 64 km
Simplifying the equation:
52t = 32(t + 2) + 64
Step 5: Solve the equation to find the value of t.
Starting with the equation from the previous step:
52t = 32t + 64 + 64
52t = 32t + 128
52t - 32t = 128
20t = 128
t = 128 / 20
t = 6.4 hours
Therefore, it takes the passenger train 6.4 hours to catch up to the freight train.
Remember to keep track of units (hours in this case) and always double-check your calculations.