The equation $y+4x=100$ represents your distance y (in meters) from the finish line x seconds after you begin your leg of a relay race. The equation $y+3.8x=97$ represents your opponent's distance from the finish line. How far do you need to run until you catch up to your opponent?

Question

Mathematics

Zachariah Leach

15 August, 23:57

The equation $y+4x=100$ represents your distance y (in meters) from the finish line x seconds after you begin your leg of a relay race. The equation $y+3.8x=97$ represents your opponent's distance from the finish line. How far do you need to run until you catch up to your opponent?

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Answers (1)

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Jasiah Norris · Answer 1

3 metres

Step-by-step explanation:

If y = distance (in meters) from the finish line

x = time in seconds after the beginning of the leg of relay race.

At x=0, when the race has not started,

From the runner's equation

y+4 (0) = 100

y=100 metres

Also, from his opponent's equation

y+3.8x=97

y + (3.8X0) = 97

y=97

The distance needed by the runner to catch up to his opponent

= 100-97 = 3 metres