The question goes as follows:
Two trains are moving toward each other at speeds 17 mph and 43 mph. How far apart are they 1 minute before they pass each other?
So I have been trying to answer this question for a while now, and it is turning out to be a little harder than I thought it would be because I am not confident with the answer that I get. I would greatly appreciate any help.
The distance between them is decreasing at a rate of 50 mph, (17+13)
So in the last minute the distance to be covered is
(1/60)(50) miles ----> recall, distance = rate x time
= 5/6 of a mile
Thank you for your response, but to clarify, why is "(17+13)" important in the problem?
Reiny I believe you have made a mistake, but using the same method, the correct answer would be 1mile (because (1/60)*(60)). But still, thanks for the help.
Well, I'm here to provide some humorous assistance! Let's see if we can solve this problem together.
First, let's convert the speeds of the trains into distances. Since they are moving toward each other, we can add their speeds to find the relative speed at which they are approaching each other.
So, the relative speed is 17 mph + 43 mph, which equals 60 mph.
Since they are traveling toward each other, we can think of them as "closing the gap" between them. If we consider that they were originally a certain distance apart, we need to find out how much distance they close in 1 minute.
Now, since we know the relative speed is 60 mph, we can convert that into miles per minute by dividing it by 60, which gives us 1 mile per minute.
Therefore, the trains close the gap by 1 mile every minute. So if we're looking for the distance 1 minute before they pass each other, they will be exactly 1 mile apart.
Voila! The trains will be 1 mile apart. I hope that brings a smile to your face while solving this problem!
To find the distance between the two trains one minute before they pass each other, we need to find the total distance covered by both trains in that time.
First, let's convert the speeds of the trains from miles per hour (mph) to miles per minute. We do this by dividing the speed by 60 (since there are 60 minutes in an hour):
Train 1 speed: 17 mph / 60 minutes = 0.2833 miles per minute
Train 2 speed: 43 mph / 60 minutes = 0.7167 miles per minute
Next, we need to calculate the distance each train covers in one minute. We can do this by multiplying the speed by the time (1 minute):
Distance covered by Train 1 in 1 minute = 0.2833 miles/minute * 1 minute = 0.2833 miles
Distance covered by Train 2 in 1 minute = 0.7167 miles/minute * 1 minute = 0.7167 miles
To find the total distance between the two trains one minute before they pass each other, we add up the distances covered by each train:
Total distance = Distance covered by Train 1 + Distance covered by Train 2
Total distance = 0.2833 miles + 0.7167 miles = 1 mile
Therefore, the two trains are 1 mile apart one minute before they pass each other.