Jeff hikes 1/4 mile every 2/5 hour. John hikes 1/2 mile every 1/7 hour.
A) Who hikes farther in one hour. Show work.
B) Who walks faster, Jeff or John. Explain your reasoning
(1/4)(20) / [(2/5)(20)] = 5 / 8
(1/2)(14) / [(1/7)(14)] = 7 / 2
5/8 mile / hour is less than 7/2 mile/ hour. John walks faster so further in an hour.
A) To determine who hikes farther in one hour, we need to find out how far each person hikes in one hour.
Let's start with Jeff. We know that Jeff hikes 1/4 mile every 2/5 hour. To find out how far he hikes in one hour, we can set up a proportion:
(1/4 mile) / (2/5 hour) = x miles / 1 hour
To solve this proportion, we can cross-multiply:
(1/4) * (1 hour) = (2/5) * x
1/4 = 2x/5
Next, we can multiply both sides of the equation by 4 to eliminate the fraction:
1 = (8/5) * x
Finally, to isolate the variable x (the distance Jeff hikes in one hour), we can divide both sides of the equation by (8/5):
x = 1 / (8/5)
x = 5/8
Therefore, Jeff hikes 5/8 mile in one hour.
Now let's calculate the distance John hikes in one hour. We know that John hikes 1/2 mile every 1/7 hour. Let's set up a proportion:
(1/2 mile) / (1/7 hour) = y miles / 1 hour
Cross-multiplying:
(1/2) * (1 hour) = (1/7) * y
1/2 = y/7
Next, multiply both sides of the equation by 2:
1 = (2/7) * y
To find y, we can multiply both sides of the equation by 7/2:
y = 1 * (7/2)
y = 7/2
Therefore, John hikes 7/2 miles in one hour.
Now we can compare the distances: Jeff hikes 5/8 mile in one hour, while John hikes 7/2 miles in one hour.
Since 5/8 is less than 7/2, John hikes farther in one hour.
B) To determine who walks faster, we compare their speeds. Speed is defined as distance traveled per unit of time.
We know that Jeff hikes 1/4 mile every 2/5 hour. To calculate his speed, we divide the distance by the time:
Speed of Jeff = (1/4 mile) / (2/5 hour)
Speed of Jeff = (1/4) * (5/2)
Speed of Jeff = 5/8 mile per hour
Similarly, we know that John hikes 1/2 mile every 1/7 hour. Let's calculate his speed:
Speed of John = (1/2 mile) / (1/7 hour)
Speed of John = (1/2) * (7/1)
Speed of John = 7/2 mile per hour
Comparing the speeds, we find that Jeff's speed is 5/8 mile per hour, while John's speed is 7/2 mile per hour.
Since 5/8 is less than 7/2, Jeff walks slower than John. Therefore, John walks faster than Jeff.