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?

Question

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?

Answer 1

time = distance/speed

he took 3 minutes (3/60 hr) longer to walk than to run, so

d/5 = 3/60 + d/10
d/10 = 3/60
d = 1/2

check:
it takes 6 min to run 1/2 km at 5km/hr
it takes 3 min to run 1/2 km at 10km/hr

Answer 2

Let's assume the distance to the train station is "d" kilometers.

Arman walks to the station at a speed of 5 km/h, so it takes him d/5 hours to reach the station.

If he had run at 10 km/h, his travel time would be d/10 hours.

We are given that he misses his train by 1 minute (1/60 hours) when walking, and he would have had 2 minutes (2/60 hours) to spare if he had run.

Using this information, we can set up the following equation:

d/5 + 1/60 = d/10 - 2/60

To simplify the equation, we can multiply through by the least common denominator (60):

12d + 1 = 6d - 2

Now let's solve for "d":

12d - 6d = -2 - 1
6d = -3
d = -3/6
d = -0.5

The distance to the station cannot be negative, so there seems to be an error in the given information or the problem statement. Please double-check the question or provide any additional information if available.

Answer 3

To find the distance to the train station, we need to use the information given about Arman's walking and running speeds, along with the time differences.

Let's assume the distance to the train station is 'd' kilometers.

We are given that Arman walks to the train station at 5 km/h. This means that if he walks d kilometers, it would take him d/5 hours to reach the station.

We are also given that Arman misses his train by 1 minute. There are 60 minutes in an hour, so 1 minute is equal to 1/60 hours. So, if Arman had reached the train station on time, it would have taken him d/5 - 1/60 hours.

Now, we are told that if Arman had run to the train station at 10 km/h, he would have had 2 minutes to spare. This means that if he ran d kilometers, it would take him d/10 hours to reach the station, and he would have arrived d/10 - 2/60 hours earlier.

Setting up the equation, we have:

d/5 - 1/60 = d/10 - 2/60

To solve this equation, we can multiply everything by 60 to clear the denominators:

12d - 1 = 6d - 2

Now, we can simplify and solve for d:

6d = 12d - 1 - 2

6d = 12d - 3

-6d = -3

d = (-3)/(-6)

d = 0.5

Therefore, the distance to the train station is 0.5 kilometers.