Arman walks to the train station at 5 Km/h. He misses his train by 1 min. If he had run at 10 Km/h, he would have had 2 min to spare. How far is it to the station?
To solve this problem, we need to set up an equation based on Arman's walking and running speeds, along with the time difference when he misses the train.
Let's assume the distance to the train station is "D" kilometers.
When Arman walks at a speed of 5 Km/h, he spends D/5 hours to reach the train station.
When Arman runs at a speed of 10 Km/h, he spends D/10 hours to reach the train station.
We are given that he misses his train by 1 minute, which is equal to 1/60 hours.
So, when Arman walks, he spends D/5 hours to reach the station, which is equal to the time it takes for the train to leave, plus 1/60 hours. This can be expressed as:
D/5 = time it takes for the train to leave + 1/60
Similarly, when Arman runs, he spends D/10 hours to reach the station, which is equal to the time it takes for the train to leave, minus 2/60 hours (the 2 minutes he would have had to spare). This can be expressed as:
D/10 = time it takes for the train to leave - 2/60
Now, we can solve these two equations to find the value of D, the distance to the station.
First, let's solve the equation D/5 = time it takes for the train to leave + 1/60 for the time it takes for the train to leave:
time it takes for the train to leave = D/5 - 1/60
Then, let's solve the equation D/10 = time it takes for the train to leave - 2/60 for the time it takes for the train to leave:
time it takes for the train to leave = D/10 + 2/60
Since both expressions represent the time it takes for the train to leave, we can set them equal to each other:
D/5 - 1/60 = D/10 + 2/60
To simplify the equation, we can multiply each term by 60 to get rid of the fractions:
12D - 1 = 6D + 2
Now, we can solve for D:
12D - 6D = 2 + 1
6D = 3
D = 3/6
D = 0.5
Therefore, the distance to the train station is 0.5 kilometers.