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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.

I got x=40, x=-50/11, but you can't have negative speed, so the turtle's speed is 40 meters per hour. After that, I just plugged in x onto one of the expressions and got 450.

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facundo3141592 facundo3141592 · Answer 2 · 2022-04-20T14:31:17+02:00

By solving a system of equations, we will see that the distance is 383m

How to find the distance between the garden and the woods?

Let's define the speeds of the animals as:

St = speed of the turtle.
Sh = speed of the hedgehog.

We know that if they leave their houses at the same time, they meet after 5 hours, so we have:

(St + Sh)*5h = D

where D is the distance we want to find.

We also know that:

St = Sh - 10m/h

And if the turtle leaves 4.5 hours earlier, they meet at 150m from the woods.

This is written as:

St*9.5h + Sh*5h = D - 150m

So we need to solve a system of equations:

St*9.5h + Sh* = D - 150m

St = Sh - 10m/h

(St + Sh)*5h = D

Replacing the second equation into the other two we get:

(Sh - 10m/h + Sh)*5h = D

(Sh - 10m/h)*9.5h + Sh*T = D - 150m

Now we can find Sh on the second one.

Sh*14.5h = D - 150m + 95m

Sh = (D + 150m + 95m)/14.5h = D/14.5h + 16.9 m/h

Replacing that on the other equation we get:

(2*(16.9m/h + D/14.5h) - 10m/h )*5h = D

118.96m + D*(10/14.5) = D

118.96m = D*(1 - 10/14.5)

D = 118.96m/(1 - 10/14.5) = 383m

The distance is 383m

IF you want to learn more about systems of equations, you can read:

https://brainly.com/question/13729904