Farmer Brown drives to town at 36 mph and returns at 48 mph. If his total driving time is 3 and 1/2 hours, how far away is the town?
since time = distance/speed,
d/36 + d/48 = 7/2
4d/144 + 3d/144 = 504/144
7d = 504
d = 72 mi
To find the distance to the town, we can use the formula:
Distance = Speed × Time
Let's assume the distance to the town is D miles.
On the way to town:
Speed = 36 mph
Time = x hours (unknown)
So the distance to the town can be expressed as:
D = 36x
On the way back from town:
Speed = 48 mph
Time = 3.5 - x hours (total driving time minus the time spent on the way to town)
So the distance back from town can be expressed as:
D = 48(3.5 - x)
Since the distance to the town and back from town is the same, we can equate the two expressions:
36x = 48(3.5 - x)
Now let's solve for x:
36x = 168 - 48x
36x + 48x = 168
84x = 168
x = 168/84
x = 2
Now we can substitute the value of x back into either equation:
D = 36(2)
D = 72
Therefore, the distance to the town is 72 miles.
To calculate the distance to the town, we can use the formula:
Distance = Speed × Time
Let's denote the distance to the town as 'D.'
Given that Farmer Brown drives to town at 36 mph and returns at 48 mph, we can set up the following equations:
D = 36 × t1 (Equation 1, where t1 is the time taken to go to town)
D = 48 × t2 (Equation 2, where t2 is the time taken to return from town)
The total driving time is given as 3 and 1/2 hours, which can be written as 3.5 hours. We can also express this as:
t1 + t2 = 3.5 (Equation 3)
Now, we have three equations with three unknowns (D, t1, and t2). To solve this system of equations, we'll use a method called substitution.
From Equation 1, we can solve for t1:
t1 = D / 36
Substituting this value of t1 into Equation 2, we have:
D = 48 × (D / 36)
Simplifying, we get:
D = 4/3 × D
Now, let's substitute the value of D from Equation 3 into this equation:
t1 + t2 = 3.5
(D / 36) + t2 = 3.5
t2 = 3.5 - (D / 36)
Substituting t2 into Equation 3, we have:
(D / 36) + (3.5 - (D / 36)) = 3.5
Now, we can solve this equation to find the value of D, which represents the distance to the town.
Simplifying and solving the equation, we get:
D / 36 + 3.5 - D / 36 = 3.5
D / 36 - D / 36 = 3.5 - 3.5
0 = 0
Since 0 = 0, this means that there is no unique solution to this problem. Therefore, we cannot determine the distance to the town with the given information.
Please note that it is possible there may be missing or incorrect information in the problem statement, as it appears to lead to an unsolvable equation.