# Algebra

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During the race, Bernie ran 9 meters every 4 seconds, while Barnaby ran 2 meters evey second and got a 10 meter head start. If the race is 70 meters long, did Bernie ever catch with Barnaby? If so, when?

I have to use a proportion to solve this.

• Algebra -

The proportion can be the speed: 9/4 = 2.25 m/s for Bernie and 20.00 m/s for Barnaby.

The distance from the starting line at time t after the start is
X1 (Barnaby) = 10 + 2 t
X2 (Benie) = 2.25 t
Bernie passes Barnaby when X1 = X2. Solve for the X where that happens.
10 + 2t = 2.25 t
10 = 0.25 t
t = 40 seconds

X1 = X2 = 90 m

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