The distance (d) a moving body travels, varies directly with the time (t) when it moves. A train travels 72 km in 2 hours. Find the equation that relates d and t.

The correct answer is $d=36t$.

Since the distance $d$ varies directly with time $t$, we can write the general form of a direct variation equation as:

$d=kt$

where $k$ is the constant of variation (also called the constant of proportionality). Our goal is to find the value of $k$.

Step 1: Use the given information to find k.

We are told the train travels 72 km in 2 hours. This gives us:

$d=72$ and $t=2$

Substitute these values into $d=kt$:

$72=k\times 2$

Step 2: Solve for k.

Divide both sides by 2:

$k=\frac{72}{2}=36$

So the constant of variation is $k=36$. This also represents the speed of the train — 36 km per hour.

Step 3: Write the final equation.

Substituting $k=36$ back into the direct variation formula:

$d=36t$

Verification: When $t=2$, we get $d=36\times 2=72$ km. ✓ This matches the given data perfectly.

Therefore, the equation that relates distance and time for this train is $d=36t$.