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Illusion [34]
3 years ago
11

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 mi

n. Write a system of linear equations that represents this situation. How long does it take to jog around the park?
Mathematics
1 answer:
stich3 [128]3 years ago
6 0
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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