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 calculate the distances he traveled by bus, jogged, and walked separately, and then add them together.
Let's say the total distance Sam traveled is represented by "x".
1/4 of the distance, which Sam traveled by bus, is given as 1/4 * x.
The remaining distance after the bus ride is represented by (x - 1/4 * x), which simplifies to (3/4 * x).
Next, Sam jogged 1/2 of the remaining distance, i.e., 1/2 * (3/4 * x).
The distance Sam walked is given as 800 feet, which is equal to the remaining distance: (3/4 * x) - 1/2 * (3/4 * x).
We can now set up an equation to solve for "x":
(3/4 * x) - 1/2 * (3/4 * x) = 800.
Let's solve it step by step:
(3/4 * x) - (3/4 * x) * 1/2 = 800.
Multiply 3/4 * x by 1/2:
(3/4 * x) - (3/8 * x) = 800.
Multiply the x terms on the left side:
(3/4 - 3/8) * x = 800.
Calculate the common denominator on the left side:
(6/8 - 3/8) * x = 800.
Simplify the fraction:
3/8 * x = 800.
To isolate x, divide both sides by 3/8:
x = 800 / (3/8).
Divide 800 by 3/8:
x = 800 * (8/3).
Multiply 800 by 8/3:
x = 1600 feet.
Therefore, the total distance Sam traveled is 1600 feet.