Based on the calculations, the distance between the garden and the woods is equal to 383 meters.
<h3>How to calculate the distance.</h3>
First of all, we would assign a variable to the different speeds of the turtle and hedgehog as follows:
- Let the turtle's speed be S₁.
- Let the hedgehog's speed be S₂.
Mathematically, distance is given by this formula:
Distance = speed × time
Translating the word problem into an algebraic expression, we have;
If they both meet in 5 hours:
D = (S₁ + S₂) × 5
D = 5S₁ + 5S₂ ......equation 1.
Turtle's speed is 10 meters per hour slower than the hedgehog:
S₁ = S₂ - 10 .....equation 2.
If the turtle had left home 4.5 hours earlier than the hedgehog had left his home:
9.5S₁ + 5S₂ = D + 150 .....equation 3.
Substituting enq. 2 into eqn. 1, we have:
D = 5(S₂ - 10) + 5S₂
D = 5S₂ - 50 + 5S₂
D = 10S₂ - 50 .....equation 4.
Equating eqn. 3 and eqn. 4, we have:
10S₂ - 50 = 9.5(S₂ - 10) + 5S₂ - 150
10S₂ - 50 = 9.5S₂ - 95 + 5S₂ - 150
10S₂ - 50 = 14.5S₂ - 245
14.5S₂ - 10S₂ = 245 - 50
4.5S₂ = 195
S₂ = 195/4.5
S₂ = 43.3 m/h.
Now, we can find the distnace:
D = 10S₂ - 50
D = 10(43.3) - 50
D = 433 - 50
D = 383 meters.
Learn more about distance here: brainly.com/question/10545161
