A train leaves Kaduna for Lagos at 64 km/h, and an express train to Kaduna leaves Lagos an hour later at 96 km/h. If the distance between Kaduna and Lagos is 624 km, how far are the trains from Lagos when they meet?
Answer (3)
Good to see you here. Now back to the train.
Kaduna, K Lagos, L
Train leaves at 64 km/h
One hour late second train leaves Lagos at 96 km/h.
At the point they meet, if first train has been travelling for "x" hours. Second train has been travelling for (x-1) hour.
At the point the meet, the total distance travelled is equal to 624 km.
Therefore:
64(x) + 96(x-1) = 624 64x + 96x - 96 = 624 160x = 624+96 160x = 720 , x = 720/160 = 4.5
So when they meet, the first train which left Kaduna has travelled= 64x = 64*4.5= 288km from Kaduna.
So it is (624-288) km from Lagos. = 336 Km from Lagos.
Second train which left Lagos has travelled = 96(x-1) = 96(4.5-1) = 336km. The second train is also 336 km away from Lagos.
Cheers.
The trains meet 336 km from Lagos.
Let's denote the time taken for the first train (from Kaduna to Lagos) as t hours. Since the second train (from Lagos to Kaduna) leaves an hour later, its time traveled will be t − 1 hours.
The distance traveled by the first train in t hours is given by the product of its speed and time:
Distance of first train = Speed of first train × t
Distance of first train = 64 km/h × t
Similarly, the distance traveled by the second train in t − 1 hours is:
Distance of second train = Speed of second train × ( t − 1 )
Distance of second train = 96 km/h × ( t − 1 )
The sum of these distances must equal the total distance between Kaduna and Lagos, which is 624 km:
64 t + 96 ( t − 1 ) = 624
Expanding the equation, we get:
64 t + 96 t − 96 = 624
Combining like terms, we have:
160 t − 96 = 624
Adding 96 to both sides to isolate the term with t , we get:
160 t = 720
Dividing both sides by 160 to solve for t , we find:
t = 160 720
t = 4.5 hours
Now, we can calculate the distance from Lagos where the two trains meet by finding the distance the first train has traveled in 4.5 hours:
Distance from Lagos = 64 km/h × 4.5 hours
Distance from Lagos = 288 km
However, since the second train is traveling faster, they will meet closer to Kaduna than this point. We need to calculate the distance the second train has traveled in t − 1 hours:
Distance of second train = 96 km/h × ( 4.5 − 1 ) hours
Distance of second train = 96 km/h × 3.5 hours
Distance of second train = 336 km
Therefore, the two trains meet 336 km from Lagos.
When the two trains meet, they are 336 km from Lagos. The time taken for the first train is 4.5 hours, and the second train, which started an hour later, has traveled for 3.5 hours. This calculation shows that the express train makes up the distance quickly due to its higher speed.
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