You can ride your bike around your block 10 times and the whole neighborhood once in 24 minutes. You can ride you bike around your block 5 times and the whole neighborhood 2 times in 18 minutes. How long does it take you to ride around the neighborhood

4 minutes

Set up 2 equations and solve

let b represent time taken to ride around block and

let n represent time taken to ride around neighbourhood, then

10b + n = 24 → (1)

5b + 2n = 18 → (2)

multiply (1) by - 2

- 20b - 2n = - 48 → (3)

add (2) and (3) term by term to eliminate n

- 15b = - 30 (divide both sides by - 15)

b = 2

substitute b = 2 into (1) and solve for n

20 + n = 24 (subtract 20 from both sides)

n = 4

Thus it takes 4 minutes to ride around the neighbourhood