Many of the immigrants settled on farm land and they had to drive to town for supplies. One farmer drives to town at 36 miles per hour and returns at 48 miles per hour. If his total driving time is 3 ½ hours, how far is his farm from town?

t + (36/48)t = 3.5hrs.

t + 0.75t = 3.5,
1.75t = 3.5,
t = 2hrs = Time to reach town.
0.75t = 1.5hrs = Time to return home.

d = v*t = 36 * 2 = 72 Miles.
Or d = 48 * 1.5 = 72 Miles.

To find the distance between the farmer's farm and the town, we need to use the formula:

Distance = Speed × Time.

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

We can determine the time it takes for the farmer to drive from the farm to town by dividing the distance by the speed. Using this, the driving time from the farm to town can be calculated as:

Time = Distance / Speed.

So, the time taken by the farmer to go from the farm to town is d / 36.

Now, let's consider the return trip from town to the farm. The speed on the return trip is 48 miles per hour. So, the driving time from town to the farm can be calculated as:

Time = Distance / Speed.

Using this information, the time taken by the farmer to return from town to the farm is d / 48.

The total driving time for the round trip is given as 3 ½ hours, or 3.5 hours.

So, we can write the equation:

d / 36 + d / 48 = 3.5.

To solve this equation, we need to find a common denominator. The least common multiple (LCM) of 36 and 48 is 144.

Multiplying every term by 144, the equation becomes:

4d + 3d = 3.5 * 144.

Combining like terms, we get:

7d = 3.5 * 144.

Now, divide both sides of the equation by 7:

d = (3.5 * 144) / 7.

Calculating this expression, we find:

d ≈ 180.

Therefore, the farm is approximately 180 miles away from the town.