If a football player can run 21 yards in 3.9 seconds, determine which of the following equations could be used to find the number of yards 𝑦 the player can run in a second. A) 3.9 plus 𝑦 equals 21, B) 21 𝑦 equals 3.9, C) 3.9 minus 𝑦 is equal to 21, D) 3.9 𝑦 equals 21, or E) 21 minus 𝑦 equals 3.9.
The first thing I want to look at is that if a player can run 21 yards in 3.9 seconds. Let’s find what 𝑦 is. Let’s find how far the player can run in one second or to work out how far the player can run in a second. 21 because that’s our yards travelled divided by 3.9, our number of seconds, this gives us that 𝑦 is equal to 5.38 seconds to two decimal places. Now, let’s substitute this into our answers so that we can see which one of them will work.
So when we look at the first answer, so we get 3.9 plus 5.38 is equal to 9.28, where it isn’t the same as 21. So therefore, this cannot be the right answer. Well, if we look at our second answer and we substitute in 5.38 for 𝑦, we get 21 multiplied by 5.38 is equal to 112.98, so not 3.9. Therefore, that can’t be correct.
Looking at answer C, so we have 3.9 minus 5.38. Well, that’s equal to negative 1.48. So again, that’s not the same as 21. So therefore, that can’t be correct. Well if we look at D though, we can see that 3.9 multiplied by 5.38 is equal to 20.982. Well, if you remember, we’ve actually rounded our value for 𝑦 to two decimal places. The answer is actually very close to 21 and would actually be 21 to two significant figures. So it’s looking very likely that this is the correct answer, but I’m just gonna check E just to make sure.
So for E, we get 21 minus 5.38, which is equal to 15.62. Well, this definitely isn’t the same as 3.9. So we can certainly say that E also isn’t correct. So therefore, we can say that the answer D must be our correct answer. And we’re gonna check that by rearranging our original equation that we used to find 𝑦.
Well, if we multiply both sides by 3.9, we’re gonna get 3.9 𝑦 is equal to 21. So yes, that proves that our answer D is correct. And actually, this is the quickest method to use to solve this kind of a problem, if you are competent to rearrange algebraically. So as I’ve said that both sounds confirmed, that yes, D is the correct answer.