A hiker is climbing at a constant rate of 2.4 miles per hour.
Part A
If d represents the distance the hiker climbed and h represents the time in hours, write an equation to model the relationship. Explain your answer.
Part B
Complete the table by determining the distance the hiker climbed in 1.5 hours and 2 hours.
Time (hours) Distance (miles)
1
2.4
1.5
2
2.5
6.0
Part C
How much time would it take for the hiker to climb 12 miles?
hours
Part A
The equation to model the relationship between distance (d) and time (h) for the hiker climbing at a constant rate of 2.4 miles per hour is:
d = 2.4h
This equation represents the distance the hiker has climbed (d) being equal to their rate of 2.4 miles per hour (the constant) multiplied by the time in hours (h).
Part B
Time (hours) Distance (miles)
1 2.4
1.5 d = 2.4 * 1.5 = 3.6
2 d = 2.4 * 2 = 4.8
2.5 6.0
Time (hours) Distance (miles)
1 2.4
1.5 3.6
2 4.8
2.5 6.0
Part C
To find out how much time (h) it would take for the hiker to climb 12 miles, we can use the equation from Part A:
12 = 2.4h
Now, we can solve for h:
h = 12 / 2.4
h = 5
So, it would take the hiker 5 hours to climb 12 miles.
Part A:
The equation that models the relationship between the distance the hiker climbed (d) and the time in hours (h) can be expressed as:
d = 2.4h
This equation shows that the distance climbed (d) is directly proportional to the time in hours (h), with a constant rate of 2.4 miles per hour.
Part B:
To determine the distance the hiker climbed in 1.5 hours and 2 hours, we can substitute the respective values of h into the equation:
For 1.5 hours:
d = 2.4 * 1.5
d = 3.6 miles
For 2 hours:
d = 2.4 * 2
d = 4.8 miles
Therefore, the distance climbed at 1.5 hours is 3.6 miles, and the distance climbed at 2 hours is 4.8 miles.
Time (hours) Distance (miles)
1 2.4
1.5 3.6
2 4.8
Part C:
To find out how much time it would take for the hiker to climb 12 miles, we can rearrange the equation:
d = 2.4h
Given that the distance (d) is 12 miles, we can substitute it into the equation:
12 = 2.4h
Now, we solve for h by dividing both sides of the equation by 2.4:
h = 12 / 2.4
h = 5
Therefore, it would take the hiker 5 hours to climb 12 miles.
Part A:
Let d represent the distance the hiker climbed and h represent the time in hours. The equation to model the relationship is:
d = 2.4h
The distance climbed (d) is directly proportional to the time (h) multiplied by the constant rate of 2.4 miles per hour.
Part B:
To determine the distance the hiker climbed in 1.5 hours and 2 hours, we can substitute the values into the equation d = 2.4h.
For 1.5 hours:
d = 2.4 * 1.5
= 3.6 miles
For 2 hours:
d = 2.4 * 2
= 4.8 miles
Time (hours) Distance (miles)
1 2.4
1.5 3.6
2 4.8
Part C:
To find out how much time it would take for the hiker to climb 12 miles, we need to rearrange the equation d = 2.4h to solve for h.
d = 2.4h
Divide both sides by 2.4:
d/2.4 = h
Substitute d = 12:
12/2.4 = h
h = 5
Therefore, it would take the hiker 5 hours to climb 12 miles.
Part A:
To model the relationship between the distance the hiker climbed and the time in hours, we can write the equation as follows:
d = r * h
Where:
- d represents the distance the hiker climbed
- r represents the rate at which the hiker is climbing (2.4 miles per hour in this case)
- h represents the time in hours
In this equation, we're simply multiplying the rate of climbing (2.4 miles per hour) by the time in hours to find the distance climbed.
Part B:
To complete the table, we can use the equation from part A and substitute different values for h to calculate the corresponding distance (d):
For 1.5 hours:
d = 2.4 * 1.5 = 3.6 miles
For 2 hours:
d = 2.4 * 2 = 4.8 miles
So, the completed table looks like this:
Time (hours) | Distance (miles)
1 | 2.4
1.5 | 3.6
2 | 4.8
Part C:
To find out how much time it would take for the hiker to climb 12 miles, we can rearrange the equation from part A as follows:
h = d / r
Now we can plug in the given distance (12 miles) and the rate (2.4 miles per hour) into this equation:
h = 12 / 2.4 = 5 hours
Therefore, it would take the hiker 5 hours to climb 12 miles.