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A turtle lives in a garden and a hedgehog lives in the woods. They leave their homes at the same time walk toward each other and meet in 5 hours. The turtle walks 10 meters per hour slower than the hedgehog. If the turtle had left home 4 1/2 hours earlier than the hedgehog had left his home, the two would meet 150m from the woods. Find the distance between the garden and the woods. PLEASE EXPLAIN WHY.

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Lanuel

Based on the calculations, the distance between the garden and the woods is equal to 383 meters.

How to calculate the distance.

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

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