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?
(1 - 1/4 - 1/2(3/4))x = 800
Let the total distance be 4x meters
1/4 = x meters = bus
Remaining = 3x meters
1/2 = 1.5x meters = jogging
Remaining = 1.5x meters = 800 meters
4x = 4 /1.5 X 800 = 3200 /1.5 = 2133.33 meters ANSWER
To find the total distance Sam traveled, we need to add up the distances he traveled by bus, while jogging, and walking.
First, let's determine the distance he traveled by bus. We are given that he traveled 1/4 of the journey by bus. So, we can find this distance by multiplying the total distance by 1/4.
Let's say the total distance of the journey is represented by 'd'. Therefore, the distance Sam traveled by bus is given by:
Distance by bus = (1/4) * d
Next, we need to find the distance Sam jogged. We know that he jogged 1/2 of the remaining distance after the bus ride. To calculate this distance, we need to subtract the distance traveled by bus from the total distance and then multiply it by 1/2.
Remaining distance = Total distance - Distance by bus
Distance jogged = (1/2) * Remaining distance
Distance jogged = (1/2) * (d - (1/4) * d)
Finally, we know that Sam walked the remaining distance. We are given that he walked 800 feet. So, we can set up an equation to find the remaining distance traveled:
Distance walked = Remaining distance
800 = d - (Distance by bus + Distance jogged)
Now, let's substitute the expressions we found for Distance by bus and Distance jogged into the equation above:
800 = d - ((1/4) * d + (1/2) * (d - (1/4) * d))
We can simplify the equation to solve for 'd':
800 = d - (1/4 * d + 1/2 * d - 1/8 * d)
800 = d - (3/8 * d)
Now, we can solve for 'd' by isolating 'd' on one side of the equation:
800 = (5/8) * d
To find the value of 'd', we can multiply both sides of the equation by (8/5):
800 * (8/5) = d
d ≈ 1280
Therefore, the total distance Sam traveled is approximately 1280 feet.