Express, in hours, minutes, and seconds, the finishing time of a marathon winner who completed the race in 8569 seconds.
In this problem, we’re given the finishing time of a marathon winner. Whereas you might expect it to be given in hours, minutes, and seconds, we’re given it in seconds. It took 8569 seconds. It’s hard to know what this means. We don’t measure every length of time in seconds. So that’s why this question asked us to express the time in hours, minutes, and seconds. We need to convert the time we’ve been given into hours, minutes, and seconds. To do this, we need to know how many seconds are in a minute and how many seconds are in one hour. We know there are 60 seconds in a minute. And we also know that there are 60 minutes in an hour. So to calculate the number of seconds in an hour, we need to find 60 lots of 60 seconds.
What fact can be used to help us? Let’s try six times six. Six sixes are 36. And so we can say 60 lots of six is 10 times more than 36; that’s 360. And so 60 lots of 60 means our answer is going to increase by 10 times again, 3600. One hour is 3600 seconds. And we can use this information now to help find the answer. The first thing we can do is to see how many whole hours there are in 8569 seconds. In other words, we need to divide 8569 by 3600. Let’s look at the thousands digits, just to give us a rough idea of what the answer might be. How many threes fit in eight? There are two threes in eight. We know three threes are nine, so that would make an answer that would be too large.
So let’s try two lots of 3600. Double 36 equals 72. And so double 36 hundreds or 3600 is 72 hundreds or 7200. This is the number of seconds in two whole hours. And we can see that this definitely fits into our time of 8569 seconds. Let’s work out what the remainder is. 8569 take away 7200 — nine take away zero is nine, six take away zero is six, five take two is three, and eight take seven is one. So at this moment, we could give our answer as two hours, 1369 seconds.
But that second number seems a little bit large. Why don’t we convert it into minutes? How many minutes are there in 1369 seconds? In other words, how many 60s are there in 1369? We can use long division to help us find the answer. We can’t find the number of 60s in one or even 13. So we need to begin by thinking about the first three digits in the number. How many 60s are there in 136? Well one 60 is 60, and if we double 60, we get 120. This is close to 136. So there are two lots of 60 in 136. But there’s a remainder. We said two lots of 60 was worth 120.
So let’s subtract these two numbers to find out what we have left. Six take away zero is six three take away two is one. And the two ones in the last column cancel each other out, so we don’t need to worry about those. We have a remainder of 16. 16 is too small. We can’t find out how many 60s there are in 16. So we can bring down our final digit to include, 169. How many sixties are there in 169? We know that there are two 60s is 120 and three 60s is 180, which is too large. So again, there are only two lots of 60 in this number.
We can write the value of two lots of 60 underneath because, again, we’re going to have to work out the remainder. Nine take away zero is nine. Six take away two equals four. And one take away one is zero. So we don’t need to worry about that. Our answer is 22 remainder 49. Sometimes, it’s easy to forget what it was we were calculating for. Remember, we were trying to find the number of minutes that there were in 1369 seconds. And the answer is 22 minutes, with a remainder of 49. And that 49 represents 49 seconds that aren’t quite another minute. And so the runner’s winning time, which was 8569 seconds can be written as two hours, 22 minutes, and 49 seconds.