Answer: The following three equations could be used to determine the rate:
x*(time there) = 3 miles
(x+1)*(time back) = 3 miles
(time there) + (time back) = 2.5 hr
Step by step (including the actual solution x):
Equation for the trip there:
x*(time there) = 3 miles
Equation for the trip back:
(x+1)*(time back) = 3 miles
And we also know that:
(time there) + (time back) = 2.5 hr
So we have three equations with three unknowns and can solve for x. Let us call
(time there): t1
(time back): t2
The solution (I skipped the gory details of solving, but you can verify by plugging the values back into the equations) is
Rate x = 2 miles/hour
(time there) = 1.5 hours
(time back) = 1 hour
Now to solve this problem, all we have to remember is the
formula for calculating the linear speed given the radial speed, that is:
v = r w
where,
v = is the linear velocity or linear speed
r = is the radius of the circular disk = (1 / 2) diameter
= (1/ 2) (2.5 inches) = 1.25 inches
w = is the radial velocity (must be in rad per time) =
7200 rev per minute
Calculating for v:
v = 1.25 inches (7200 rev per minute) (2 π rad / 1 rev)
v = 56,548.67 inches / minute
Converting to miles per hour:
v = 56,548.67 inches / minute (1 mile / 63360 inches) (60
min / hour)
<span>v = 53.55 mile / hour</span>
Let x = speed and y = distance
y = x * 45
y = (x - 4) * 70
45x = 70x - 280
-25x = -280
x = 11.2
Put it back into the first equation:
y = 11.2 x 45
y = 504miles
Hope this helps! Any questions let me know :)
The answer stays in school kids I'm not really sure on the answer to ask your teacher.
