Caden exercises daily by walking on a treadmill. He sets the machine so that he will walk at a steady rate of 3.6 miles per hour.
If t represents time in hours and d represents distance in miles, write an equation that models the relationship between these variables.
Use your equation to calculate the distance Caden will walk in
3
4
of an hour.
Use your equation to calculate how long it will take for Caden to walk 4.32 miles.
The equation that models the relationship between time and distance is d = rt, where d is the distance, r is the rate, and t is the time. In this case, r = 3.6 miles per hour, so the equation is:
d = 3.6t
To find the distance Caden will walk in 3/4 of an hour, plug 3/4 into the equation for t:
d = 3.6(3/4)
d = 2.7 miles
To find how long it will take Caden to walk 4.32 miles, plug 4.32 into the equation for d and solve for t:
4.32 = 3.6t
t = 4.32 / 3.6
t ≈ 1.2 hours
To write an equation that models the relationship between time (t) and distance (d), we need to understand that distance equals rate multiplied by time. In this case, Caden is walking at a steady rate of 3.6 miles per hour.
Therefore, the equation that models this relationship is:
d = r * t
where d represents distance in miles, r represents the rate (or speed) in miles per hour, and t represents time in hours.
Now, let's use this equation to calculate the distance Caden will walk in 3/4 of an hour:
- Substituting the given rate (r = 3.6 mph) and time (t = 3/4 hour) into the equation, we get:
d = 3.6 * (3/4)
- Simplifying the equation:
d = 2.7 miles
So, Caden will walk 2.7 miles in 3/4 of an hour.
Next, let's use the equation to calculate how long it will take for Caden to walk 4.32 miles:
- Substituting the given distance (d = 4.32 miles) into the equation, we get:
4.32 = 3.6 * t
- Solving for t (time):
t = 4.32 / 3.6
- Simplifying the equation:
t = 1.2 hours
So, it will take Caden 1.2 hours to walk 4.32 miles.
The equation that models the relationship between time (t) in hours and distance (d) in miles is:
d = 3.6t
To calculate the distance Caden will walk in 3/4 of an hour:
d = 3.6 * (3/4)
= 2.7 miles
Therefore, Caden will walk 2.7 miles in 3/4 of an hour.
To calculate how long it will take for Caden to walk 4.32 miles:
d = 4.32
4.32 = 3.6t
Divide both sides of the equation by 3.6:
t = 4.32 / 3.6
= 1.2 hours
Therefore, it will take Caden 1.2 hours to walk 4.32 miles.