About how much faster was Albert than Josh?

Question

Albert ran a race $17.6$ seconds. Josh ran the race in $18.307$ seconds. About how much faster was Albert than Josh?

This is homework for a 5th grader. It's subtracting and rounding. There is no other information given from the teacher.

My son worked it out the way the teacher told him and he got 0. But when I worked it out I got .707 which rounds to .71 of a second. I asked a few ppl I know, one is a math professor, an Engineer, and a college student. All come up with the same answer as I did.. .71 of a second faster. My son's teacher said it was wrong and it was 0 seconds faster which means they tied the race.

Answer 1

Albert completes $1$ race per $17.6$ seconds. Josh completes $1$ race per $18.307$ seconds. The difference in their rates then is $$ \left|\frac{1 \;\text{race}}{17.6 \;\text{seconds}} - \frac{1 \;\text{race}}{18.307 \;\text{seconds}}\right| = \left|\frac{0.056\overline{81} \;\text{races} \;-\; 0.054624 \;\text{races}}{1 \;\text{second}}\right| \approx 0.00219 \frac{\text{races}}{\text{second}} $$

So Albert is about $0.0022 \frac{\text{races}}{\text{second}}$ faster than Josh.

Answer 2

Fascinating story! Of course there is nothing wrong with your computation, given that you want to express the difference between the racers in seconds per race. The question is: what did the teacher and your son do to get to zero.

You said your son managed to get 0 as an answer, so clearly the best way to get the answer to that queston is by asking him to show you again how he did the computation!

In the mean time we can speculate...

I can think of two possibilities.

1. They don't want to express the difference in seconds per race, but as an actual speed. That means: as races per seconds, as calculated by Mike above, or in a somewhat more natural sounding unit, like meters per seconds. Of course the latter is only possible if the numbers of meters in the racing track is given! Suppose they are running over 100 meters, then the difference in speed is 0.219 m/s (obtained by multiplying Mike's answer by 100) which could be rounded down to zero.

This theory has some disadvantages: it requires more advanced math, it requires more information than you said there was and computing actual speed and then rounding it to the nearest integer is an odd way to talk about racing which is rarely seen at the Olympics for instance.

On the other hand: the question asks 'how much faster', not 'how much earlier' which suggests we are looking for speeds rather than time differences.

2. There is a mistake: both racing times were first rounded to the nearest integer (18 seconds in both cases) and THEN substracted. This would be WRONG. In fact this is a textbook example of why one should only do the rounding at the very end, after ALL other operations have been carried out.

Perhaps there are more scenario's, I'd like to read them.

Answer 3

I know this is a fifth grade homework question, but the actual (scientific) answer to this would be 0.7 seconds faster, assuming that you use the word 'faster' to mean the difference in time. This is because the measurement 17.6 has only one significant figure. Because of this, you would have to ignore the digits after the tenths place in the measurement 18.307 seconds. This gives 18.3 seconds, and the difference between the two measurements 18.3 seconds and 17.6 seconds is 0.7 seconds.