# Video: Comparing the Speeds of Two Runners given the Distances and the Times Taken in Seconds and in Minutes

Runner A travels 75 meters in 13 seconds. Runner B travels 88 meters in 0.4 minutes. Which runner is faster?

02:26

### Video Transcript

Runner A travels 75 meters in 13 seconds. Runner B travels 88 meters in 0.4 minutes. Which runner is faster?

In order to compare the speeds of the two runners, we need to calculate the rate at which they are running, the number of meters run per second. To find this, we need to divide the number of meters that they travel by the number of seconds that it took them.

Runner A travels 75 meters in 13 seconds. So their rate, the number of meters run per second, is equal to 75 over 13. As a mixed number, this is equal to five and 10 over 13. So the rate at which runner A is travelling is five and 10 over 13 meters per second.

For runner B, it’s a little more complicated, as their time has been given in minutes, not seconds. We need to convert it to seconds first. Remember that one minute is equal to 60 seconds. And therefore, 0.4 minutes is equivalent to 0.4 multiplied by 60 seconds. We multiply both sides of this ratio by 0.4.

To perform this multiplication, we can think of 60 as 10 multiplied by six. 0.4 multiplied by 10 is four, and then multiplied by six, we have 24. So 0.4 minutes is equivalent to 24 seconds.

Now we’re able to calculate the rate at which runner B travels. They travel 88 meters in 24 seconds. So the rate is 88 over 24. The numerator and denominator of this fraction have a common factor of eight. So dividing both parts by it gives a simplified fraction of 11 over three.

As a mixed number, this is equivalent to three and two-thirds. So the rate at which runner B travels is three and two-thirds meters per second. Now we compare the two rates. Five and 10 over 13 is greater than three and two-thirds. And therefore, runner A is faster.