sam travelled 1/4 of a journey by bus. He jogged 1/2 of the remaining distance and walked the rest of the way. If he walked 800 feet, what was the total distance he traveled?
done
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To find the total distance Sam traveled, we need to break down the information provided.
Let's assume the total distance he traveled is represented by "D" (in feet).
Given:
Sam traveled 1/4 of the journey by bus.
This means he covered 1/4 * D distance by bus.
After traveling by bus, he jogged 1/2 of the remaining distance.
The remaining distance after traveling by bus is 3/4 * D (since 1 - 1/4 = 3/4).
So, the distance he jogged is 1/2 * (3/4 * D) = 3/8 * D.
Finally, after jogging, Sam walked the rest of the way, which is equal to 800 feet.
Therefore, the remaining distance after jogging is 800 feet.
We can set up the following equation to solve for D:
3/4 * D - 3/8 * D = 800
To simplify the equation, we can find the common denominator for 4 and 8, which is 8.
So, the equation becomes:
6/8 * D - 3/8 * D = 800
Now, let's combine the terms:
3/8 * D = 800
To isolate D, we can multiply both sides of the equation by 8/3:
D = (800 * 8) / 3
Calculating that, we have:
D = 6400 / 3 ≈ 2133.33 feet
Therefore, the total distance Sam traveled is approximately 2133.33 feet.