Question

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. in one particular pair of markings, r is 60 mph when t is 5 seconds. find the speed of a car that travels the given distance in 7 seconds.

r = \boxed{} mph (round to the nearest whole number.)

Explanation:

Step1: Recall inverse variation formula

For inverse variation, the relationship is \( R=\frac{k}{T} \), where \( k \) is the constant of variation.

Step2: Find the constant \( k \)

We know that when \( R = 60 \) mph and \( T = 5 \) seconds, substitute these values into the formula:
\( 60=\frac{k}{5} \)
Multiply both sides by 5 to solve for \( k \):
\( k = 60\times5=300 \)

Step3: Find the speed for \( T = 7 \) seconds

Now that we have \( k = 300 \), use the formula \( R=\frac{k}{T} \) with \( T = 7 \) seconds:
\( R=\frac{300}{7}\approx42.86 \)
Round to the nearest whole number.

Answer:

43