# Question Video: Finding the Length of a Tunnel Based on the Speed- Time- and Distance of a Passing Train Mathematics

A train traveling with a uniform speed of 180 km/h passed through a tunnel in 18 seconds. Given that the train was 210 meters long, find the length of the tunnel.

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### Video Transcript

A train traveling with a uniform speed of 180 kilometers per hour passed through a tunnel in 18 seconds. Given that the train was 210 meters long, find the length of the tunnel.

So to solve this problem, what we’re going to be using is our speed–distance–time formulae. And we can work out what we’re going to use using our speed–distance–time triangle. So here we can see that distance is equal to speed multiplied by time. Speed is equal to distance over time. And time is equal to distance over speed.

So in this question, what we’re looking to find is the length of the tunnel. So what we’re looking for is a distance. So we’re gonna be using distance is equal to speed multiplied by time. So the first thing we’re gonna do is work out the total distance traveled by the train. However, we don’t know what the distance is. But what we do know is that the speed is equal to 180 kilometers per hour and the time is equal to 18 seconds.

Well, what we always do now before we do any calculations is check the units. And we can see here that the speed is in 180 kilometers per hour. However, our time is in seconds. So what we need to do is find out what our time in seconds is as hours. Well, one way of thinking about how we can work this out would be to divide 18 by 60, because that would convert it into minutes, and then divide it by 60 again. And that’s because there are 60 minutes in an hour. And in fact, what we’d be doing is do 18 divided by 3600. And that’s because 60 multiplied by 60 is 3600. And also we know that there are 3600 seconds in an hour. And when we do that, we get 0.005 hours.

Okay, great, so we now have our time in hours as well. So we’ve got our units the same. So what we can now do is use our formula to work out the distance traveled by the train. And that’s because the distance is gonna be equal to 180 multiplied by 0.005, which is gonna be equal to 0.9. But what are our units?

Well, we can see from the question that the speed was in kilometers per hour. So therefore, our unit’s gonna be kilometers. So now the distance that the train has traveled is 0.9 kilometers. Well, what we’re trying to find is the length of the tunnel. And we’re given that the train was 210 meters long. So therefore, here we’re looking at meters. So what we want to do is we want to convert our 0.9 kilometers into meters.

Well, therefore, we know that the distance is gonna be 900 meters. And that’s because we used one of our other conversion factors, which is that one kilometer is equal to 1000 meters. So we’ve done 0.9 multiplied by 1000, which is 900.

So therefore, the length of the tunnel is gonna be equal to the total distance traveled by the train minus the length of the train itself, which is 900 minus 210, which is gonna give us a final length of the tunnel of 690 meters.

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