A person travels between two towns. At 60 km/h, he arrives 1.5 hours early. At 40 km/h, he arrives 1 hour late. What is the distance between the towns?

Correct Answer: Option 1) 300 km

To find the distance between the two towns, we can set up an algebraic equation based on the time taken at two different speeds.

Let the distance between the two towns be $d$ km, and let the scheduled or ideal time to complete the journey be $t$ hours.

We know the formula relating distance, speed, and time is:

$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

Case 1: Traveling at a speed of 60 km/h, the person arrives 1.5 hours early. Therefore, the time taken for this journey is $t-1.5$ hours.

$\frac{d}{60}=t-1.5$

$t=\frac{d}{60}+1.5$     --- (Equation 1)

Case 2: Traveling at a speed of 40 km/h, the person arrives 1 hour late. Therefore, the time taken for this journey is $t+1$ hours.

$\frac{d}{40}=t+1$

$t=\frac{d}{40}-1$     --- (Equation 2)

Since both expressions equal $t$, we can equate Equation 1 and Equation 2:

$\frac{d}{40}-1=\frac{d}{60}+1.5$

Now, rearrange the terms to solve for $d$:

$\frac{d}{40}-\frac{d}{60}=1.5+1$

$\frac{d}{40}-\frac{d}{60}=2.5$

Find a common denominator for 40 and 60, which is 120:

$\frac{3d-2d}{120}=2.5$

$\frac{d}{120}=2.5$

Multiply both sides by 120:

$d=2.5\times 120$

$d=300\text{km}$

Thus, the distance between the two towns is 300 km.