Question

The last part of one triathlon is a 10K (10 kilometers or 10,000 meters) run. When runner Ana starts this last running part, she is 600 meters behind runner Bea. But Ana can run faster than Bea: Ana can run (on average) 225 meters each minute, and Bea can run (on average) 200 meters each minute. Who wins, Ana or Bea? If Ana wins, when does she catch up with Bea? If Bea wins, how far behind is Ana when Bea finishes?

Answer 1

Answer:

Ana wins by about 2.5 minutes.

Step-by-step explanation:

Bea:

10,000-600=9,400

9,400/200= 47minutes to finish

Ana:

10,000/225=44.44minutes to finish

Answer 2

Answer:

A). Ana will win the race.

B). Ana will catch up Bea after 24 minutes.

Step-by-step explanation:

A). Length of the last part of the race = 10000 meters

Bea runs with the speed = 220 meters per minute

Since Bea is 600 meters ahead of Ana then distance to cover by Bea = 10000 - 600 = 9400 meters

Now times taken by Bea to cover the remaining distance = $\frac{\text{Distance}}{\text{Speed}}$  

= $\frac{9400}{200}$

= 47 minutes

Ana has to cover the distance = 10000 meters

Speed of Ana = 225 meters per minute

Time to cover this distance =  $\frac{10000}{225}$

                                             = 44.44 minutes

Therefore, Ana will win the race.

B). Relative speed of Ana = 225 - 200 = 25 meters per second

To cover the distance between Ana and Bea = 600 meters

Time taken to cover 600 meters with the relative speed of anna

= $\frac{600}{25}$

= 24 minutes

Therefore, after 24 minutes Ana will catch up with Bea.