Question

1. the equation ( d = 27.8t ) shows the direct - variation relationship between the time and maximum legal distance traveled on most two - lane highways in canada. the variable ( t ) represents the time in seconds, and ( d ) represents the distance in meters. use the equation to answer the questions.

a. what distance can a car legally cover in 30 seconds? in 1 hour?
b. what is the shortest amount of time in which a person can legally drive 15 kilometers? (( 1mathrm{km}=1000mathrm{m} ))
c. what is the legal speed limit on most two - lane canadian highways in meters per second? in kilometers per hour? in miles per hour? (( 1mathrm{mi}approx1.6mathrm{km} ))

Explanation:

Step1: Find distance in 30 seconds

Substitute \(t = 30\) into \(d=27.8t\).
\(d = 27.8\times30=834\) meters.
Since \(1\) hour \(=3600\) seconds, substitute \(t = 3600\) into \(d = 27.8t\).
\(d=27.8\times3600 = 100080\) meters.

Step2: Find shortest time for 15 km

First, convert \(15\) km to meters: \(15\times1000 = 15000\) meters.
Then, use \(t=\frac{d}{27.8}\), so \(t=\frac{15000}{27.8}\approx539.57\) seconds.

Step3: Convert speed limit

The speed formula is \(v=\frac{d}{t}\). From \(d = 100080\) meters and \(t = 3600\) seconds, \(v=\frac{100080}{3600}=27.8\) m/s.
To convert to km/h: \(27.8\times3.6 = 100.08\) km/h.
To convert to mi/h: \(\frac{100.08}{1.6}=62.55\) mi/h.

Answer:

a. In 30 seconds: \(834\) meters; in 1 hour: \(100080\) meters.
b. Approximately \(539.57\) seconds.
c. \(27.8\) m/s, \(100.08\) km/h, \(62.55\) mi/h.