Final answer:
By setting up equations based on given speeds and times and solving them simultaneously, we find that the turtle's speed is 40 meters per hour, the hedgehog's speed is 50 meters per hour, and the distance between the garden and the woods is 450 meters.
Step-by-step explanation:
Let's denote the turtle's speed as T meters per hour and the hedgehog's speed as H meters per hour. We know that the turtle walks 10 meters per hour slower than the hedgehog, so we have H = T + 10.
When they meet in 5 hours after leaving their homes at the same time, they would have covered the entire distance between the garden and the woods together. Since speed multiplied by time gives us distance, we can express this as 5T + 5H equals the distance between the garden and the woods.
If the turtle had left 4 and a half hours earlier, it would have covered an additional distance of 4.5T meters. In that scenario, they would meet 150 meters from the woods. This gives us the second equation: 4.5T + 5T + 5H = Distance - 150.
Substitute H with T + 10 in the equations and solve them simultaneously:
- 5T + 5(T + 10) = Distance
- 4.5T + 5T + 5(T + 10) = Distance - 150
The first equation simplifies to 10T + 50 = Distance.
The second equation simplifies to 14.5T + 50 = Distance - 150.
Setting both equations equal to each other gives us 14.5T + 50 = 10T + 50 + 150.
Solving the equation yields T = 40 meters per hour for the turtle's speed, and consequently, H = 50 meters per hour for the hedgehog.
Substitute T back into any of the distance equations, say 10T + 50 = Distance, gives us 400 + 50 = 450 meters as the distance between the garden and the woods.