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 59 mph when t is 5 seconds. find the speed of a car that travels the given distance in 6 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. First, find \( k \) using the given values \( R = 59 \) mph and \( T = 5 \) seconds.
\( 59=\frac{k}{5} \)
Multiply both sides by 5: \( k = 59\times5 = 295 \)

Step2: Find speed for \( T = 6 \) seconds

Now use the same \( k \) to find \( R \) when \( T = 6 \) seconds. Using \( R=\frac{k}{T} \) with \( k = 295 \) and \( T = 6 \):
\( R=\frac{295}{6}\approx49.17 \)
Rounding to the nearest whole number, \( R\approx49 \)

Answer:

49