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?

Let x = distance to town, t1 = time to town and t2 = return time.

x = v1t1 = v2t2 so
36t1 = 48t2 Which seems like you can't solve it. But t2 = 3.5 - t1. So
36t1 = 48(3.5-t1). Solve for t1 and put back into x = 36(t1)

To find the distance between Farmer Brown's farm and the town, we need to calculate the driving time for each leg of the trip.

Let's assume the distance between the farm and the town is "d" miles.

We know that the driving time is equal to the distance divided by the speed.

For the first leg, the driving time is d/36 hours.

For the return trip, the driving time is d/48 hours.

The total driving time is given as 3 and 1/2 hours, which can also be written as 7/2 hours.

So we can set up the following equation:

d/36 + d/48 = 7/2

To simplify the equation, we can find the least common denominator (LCD) of 36 and 48, which is 144. Multiplying each term in the equation by the LCD yields:

4d + 3d = 72

Combining like terms, we get:

7d = 72

Dividing both sides of the equation by 7, we find:

d = 10.286

Therefore, the distance between Farmer Brown's farm and the town is approximately 10.286 miles.

To find the distance to the town, we can use the formula:

Distance = Speed x 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 equation based on the formula mentioned above:

D/36 + D/48 = 3.5

To solve this equation, let's first find a common denominator for the fractions. The least common multiple of 36 and 48 is 144.

Multiply every term in the equation by 144 to eliminate the denominators:

(144*D)/36 + (144*D)/48 = 3.5 * 144

Simplifying the equation gives:

4D + 3D = 504

Combine the like terms:

7D = 504

Now we can solve for "D," the distance to the town:

D = 504/7

D = 72

Therefore, the town is 72 miles away from Farmer Brown's location.