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The total time for a two member team in a 5160- meter relay race is 16 minutes. The first runner on the team averages 300 meters per minute and the second runner averages 360 meters per minute. How many minutes did the first runner keep the baton before passing it to the second runner?

Answers and Views:

Answer by morgan
Let:
r1 = rate of first runner
t1 = time taken by first runner
r2 = rate of second runner
t2 = time taken by second runner

Using:
rate * time = distance

Given:
r1 = 300m/min
r2 = 360m/min
t1 + t2 = 16

Solve the time equation for t1:
t1 = 16 – t2

The total distance is the sum of each runner’s distance.
The distance for each runner is simply their rate * time.
r1*t1 + r2*t2 = 5160

Substitute in the given values for their rates:
300*t1 + 360*t2 = 5160

Substitute in the equation for t1:
300*(16 – t2) + 360*t2 = 5160

Solve for t2:
4800 – 300*t2 + 360*t2 = 5160
60*t2 = 360
t2 = 360/60
t2 = 6

Solve for t1:
t1 = 16 – t2
t1 = 16 – 6
t1 = 10

Answer:
Runner #1 ran for 10 minutes
Runner #2 ran for 6 minutes

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