Pairs of markings, a set distance apart, are made on highways so that police can detect drivers exceeding the speed limit. Over a fixed distance, the speed $R$ varies inversely with the time $T$. For one particular pair of markings, $R$ is 56 mph when $T$ is 9 seconds. Find the speed of a car that travels the given distance in 7 seconds. \[ \mathrm{R}=\square \mathrm{mph} \] (Round to the nearest whole number.)

Step 1 ：Given that the speed \(R\) varies inversely with the time \(T\), we can express this relationship as \(R = \frac{k}{T}\), where \(k\) is the constant of variation.

Step 2 ：Given that \(R = 56\) mph when \(T = 9\) seconds, we can find the constant of variation \(k\) by multiplying these values. So, \(k = R \times T = 56 \times 9 = 504\).

Step 3 ：We are asked to find the speed of a car that travels the given distance in 7 seconds. We can find this by substituting \(T = 7\) seconds and \(k = 504\) into the equation \(R = \frac{k}{T}\). So, \(R = \frac{504}{7} = 72\) mph.

Step 4 ：Final Answer: The speed of a car that travels the given distance in 7 seconds is \(\boxed{72}\) mph.