You can jog around the block twice and the park once in 10 min. you can jog around the block twice and the park 3 times in 22 min. write a system of linear equations that represents this situation. how long does it take to jog around the park?

B = block     p = park

2b + p = 10 min                2 runs around the block takes 10 minutes
2b + 3p = 22 min        2 runs around the block plus 3 runs around the park                                                       takes 22 minutes

To solve, I will use substitution. First, I will divide the first equation by 2 to get b by itself and subtract p from both sides to get b by itself. Then, substitute 5 - 1/2p in for b in the second equation because they have equal values. Then, subtract 10 from both sides to eliminate it. Divide by 2 to both sides to get 'p' by itself.

2b + p = 10 min →b + 1/2p = 5 → b = 5 - 1/2p

2(5 - 1/2p) + 3p = 22 → 10 -p + 3p = 22 → 10 + 2p = 22

10 + 3p = 22 → 2p = 12

2p = 12 → p = 6

It takes 6 minutes to jog around the park

Hope this helps!

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