An obstacle course for an endurance competition is set up such that only 50% of the competitors who start the race do not make it past the first obstacle. Of those who do, 65% make it past the second obstacle. The final obstacle is the toughest and only one third of those who complete the second obstacle are able to get past the third obstacle and finish the race. If 13 people finish the race, how many contestants started the race? 60 66 90 120 144

Question

Mathematics

Yasmin Russo

26 May, 16:31

An obstacle course for an endurance competition is set up such that only 50% of the competitors who start the race do not make it past the first obstacle. Of those who do, 65% make it past the second obstacle. The final obstacle is the toughest and only one third of those who complete the second obstacle are able to get past the third obstacle and finish the race. If 13 people finish the race, how many contestants started the race? 60 66 90 120 144

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Answers (1)

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Brenton Chavez · Answer 1

120 contestants

Step-by-step explanation:

Let the number of people who started the race=x

Only 50% of the competitors who start the race do make it past the first obstacle,

Therefore 50% of x proceed to the second obstacle.

50% of x = 0.5x

If 65% make it past the second obstacle.

Number of those who made it to the third obstacle = 65% of 0.5x = 0.325x

Since only one third of those who complete the second obstacle are able to get past the third obstacle and finish the race.

Number who finish the race

= ⅓ of 0.325x

Since 13 people finish the race,

⅓ of 0.325x = 13

0.325x = 13 X 3

x = 39/0.325

x=120

120 contestants started the race.