A cyclist travels to a neighboring town at a speed of 12 km/h and returns along the same route at a speed of 8 km/h. If the round trip takes a total of 5 hours, find the distance between his starting point and the town.

The correct option is 24 km.

Step-by-step explanation:

Step 1: Define the given variables.
Let the distance between the starting point and the town be $d$ km.
Speed on the onward trip = 12 km/h
Speed on the return trip = 8 km/h
Total time for the round trip = 5 hours

Step 2: Express the time taken for each leg of the trip.
Using the fundamental relationship $\text{Time}=\frac{\text{Distance}}{\text{Speed}}$:

Time for onward trip = $\frac{d}{12}$ hours

Time for return trip = $\frac{d}{8}$ hours

Step 3: Set up the equation for total time.
The sum of onward time and return time equals the total time of 5 hours:

$\frac{d}{12}+\frac{d}{8}=5$

Step 4: Solve the equation for $d$.
Find the least common multiple (LCM) of the denominators 12 and 8, which is 24. Rewrite the fractions with a common denominator of 24:

$\frac{2d}{24}+\frac{3d}{24}=5$

Combine the numerators:

$\frac{5d}{24}=5$

Multiply both sides by 24:

$5d=5\times 24$

$5d=120$

Divide both sides by 5:

$d=\frac{120}{5}=24$

Therefore, the distance between the starting point and the town is 24 km.