Question

On return from a business trip Mr. X was to be picked up from the railway station by his coachman. However, his meeting having finished before schedule, he left his destination earlier by catching an earlier train as a result of which he arrived 2 hours early. Immediately on arrival he ring up home for the coach and was told that it had must left in order to be exactly in tie for the train by which he was scheduled to come. To save time he started walking home ward a 4 mph. On the way he met the coachman who brought him home an hour before schedule. How far is Mr. Xs house from the railway station?

a. 12 miles
b. 16 miles
c. 8 miles
d. 24 miles

Answer 1

Mr. X walked for 3 hours at a speed of 4 mph after arriving 2 hours early and was still 1 hour ahead of schedule when he met the coach. Therefore, he walked a total of 12 miles, which is the distance from the railway station to his home. Therefore, the correct option is A.

Step-by-step explanation:

The problem about Mr. X's distance from the railway station to his house is a classic time and distance problem often found in mathematics. To solve this problem, one must establish the rate at which different events occur and the times at which they do so.

Mr. X was supposed to arrive 2 hours later than he actually did, and he started walking home at a pace of 4 mph. When he met the coachman on the way, he was still 1 hour ahead of schedule. We can calculate the distance using the relative speeds and times.

Let's assume the distance from the railway station to Mr. X's home is 'd' miles. The coach left to pick him up exactly at the time he originally should have arrived, so it left 2 hours after Mr. X started walking.

Because the coach caught up with Mr. X in less than 2 hours (since Mr. X arrived home 1 hour earlier than scheduled), we know that Mr. X walked for 3 hours in total (1 hour saved plus 2 hours early arrival). In 3 hours, at 4 mph, Mr. X would have walked 12 miles.

Therefore, Mr. X's house is 12 miles from the railway station, making option a the correct choice.