Question

1. the maximum posted speed limit on the u.s. interstate highway system may be found in rural areas of several western states. this maximum speed is 75 miles per hour or 121 kilometers per hour. what is the distance in kilometers, traveled by a car moving continuously at this speed for 3 hours and 20 minutes?
2. various types of tree sloths share the honor of being the slowest moving mammals. an average tree sloth moves with speed of 0.743 m/sec. how long does it take a sloth to move at this speed to travel 22.30 meters?

Explanation:

Step1: Convert time to seconds

First, convert 20 minutes to seconds. Since 1 minute = 60 seconds, 20 minutes = \(20\times60 = 1200\) seconds. The total time \(t\) in seconds for 3 hours and 20 minutes: 3 hours = \(3\times3600=10800\) seconds, so \(t = 10800 + 1200=12000\) seconds.

Step2: Use the speed - distance formula

The speed formula is \(d = vt\), where \(v = 121\) km/h. But we can also use the fact that if we consider the units, we know that distance \(d\) (in km) is given by \(d=v\times t\) (where \(v\) is in km/h and \(t\) is in hours). \(t = 3+\frac{20}{60}=3+\frac{1}{3}=\frac{9 + 1}{3}=\frac{10}{3}\) hours. Then \(d=121\times\frac{10}{3}=\frac{1210}{3}\approx403.33\) km.

Step3: For the sloth problem

Use the formula \(t=\frac{d}{v}\), where \(d = 22.30\) m and \(v=0.743\) m/s. Then \(t=\frac{22.30}{0.743}\approx30\) s. Convert seconds to minutes: since 1 minute = 60 seconds, \(t=\frac{30}{60}=0.5\) minutes.

Answer:

For the car: The distance is approximately \(\frac{1210}{3}\approx403.33\) kilometers. For the sloth: It takes 0.5 minutes.