Jack finished a sponsored run in 53 minutes 25 seconds. Ally finished three minutes 50 seconds after Jack. How long did Ally take in minutes and seconds? And then there is a second part to the problem: Layla finished the race eight minutes 45 seconds before Jack. How long did Layla take in minutes and seconds?
So this problem is all about children having a sponsored run. And there are two parts to the problem that we need to solve. Firstly, we’re asked to calculate how long Ally took and then secondly how long Layla took. And as we’ll see, both Ally and Layla’s times are linked to Jack’s time. So Jack’s time of 53 minutes 25 seconds is very important.
Let’s consider Ally to start with. We’re told that Ally finished three minutes and 50 seconds after Jack. So to find the answer, we need to add three minutes and 50 seconds to Jack’s time of 53 minutes 25 seconds. We can do this by adding the number of minutes first and then the number of seconds. 53 plus three equals 56 minutes. 25 plus 50 equals 75 seconds.
But if we write down that Ally took 56 minutes 75 seconds, this isn’t an accurate way of writing down the time. 75 seconds is more than a minute. So we need to split that up into minutes and seconds. We know that there are sixty seconds in a minute. So we can partition 75 seconds into one minute and 15 seconds because 60 plus 15 equals 75. Now, all we need to do is to add 56 minutes and one minute 15 seconds to find the answer. Ally takes 57 minutes and 15 seconds to complete the sponsored run.
Now, let’s think about Layla. Again, we’re given a fact that compares Layla’s time with Jack’s time. We’re told that Layla finishes the race eight minutes 45 seconds before Jack. So to calculate this answer, we need to subtract eight minutes and 45 seconds from Jack’s time of 53 minutes 25 seconds.
We can subtract eight minutes from 53 minutes quite easily. But to subtract 45 seconds is going to need a little bit of thought. There are two ways we could find the answer. Firstly, let’s think about the time that we have to subtract. What is eight minutes and 45 seconds near to? Well, it’s only 15 seconds away from nine minutes.
What if we start with Jack’s time of 53 minutes 25 seconds and then we subtract nine minutes? Well, 53 take away nine is 44. So this take us to 44 minutes 25 seconds. That was easy enough to do. But remember we subtracted nine minutes and we were only supposed to subtract eight minutes and 45 seconds. We’ve taken away 15 seconds more than we needed to. So we need to add 15 seconds to our answer. 25 seconds plus 15 seconds equals 40 seconds. And so our overall answer is 44 minutes 40 seconds.
Another way that we could subtract eight minutes and 45 seconds is to think carefully about how we could partition the 45 seconds. We can start with 53 minutes and 25 seconds. And we can see that if we subtract 25 seconds, this will take us to 53 minutes. So we can partition the 45 seconds that we need to take away into one jump of 25 and another of 20 seconds. 53 minutes take away 20 seconds equals 52 minutes and 40 seconds because we know that 40 seconds plus 20 seconds equals one minute.
Now that we’ve subtracted the 45 seconds, we just need to take away the number of minutes. 52 minutes take away eight minutes equals 44 minutes. And so, the overall answer is 44 minutes and 40 seconds.
We had to compare both parts of the problem with Jack’s original time of 53 minutes 25 seconds. In the first part, we were told that Ally finished three minutes 50 seconds after Jack. And so, we had to work out an addition to find the answer. We added the number of minutes and the number of seconds separately. But we had to remember to convert 75 seconds into one minute and 15 seconds. We can bind both parts together to find the overall answer.
In the second part of the problem, we were told that Layla finished eight minutes 45 seconds before Jack. So this time, we knew we had to subtract to find the answer. Because 45 was greater than 25, we knew we couldn’t just subtract the number of seconds and then the number of minutes. We’d have to think a bit more carefully. We could see that eight minutes 45 seconds was very close to nine minutes.
So one way we could find the answer was to subtract nine minutes and then adjust the answer by adding 15 seconds. Another method we looked at was to subtract the seconds and then the number of minutes, but to subtract the seconds in steps so that we subtracted 25 seconds to take us to a whole number of minutes and then subtracted the remaining 20 seconds.
And so, in the sponsored run, Ally took 57 minutes 15 seconds and Layla took 44 minutes 40 seconds.