Question

an object is moving at a speed of 8 yards every 9.5 days. express this speed in kilometers per month. round your answer to the nearest hundredth.
note you must use these exact conversion factors to get this question right.
distance / length\ttime
1 foot (ft) = 12 inches (in)\t1 minute (min) = 60 seconds (sec)
1 yard (yd) = 3 feet (ft)\t1 hour (hr) = 60 minutes (min)
1 mile (mi) = 5280 feet (ft)\t1 day (day) = 24 hours (hr)
1 meter (m) = 100 centimeters (cm)\t1 week (wk) = 7 days (days)
1 kilometer (km) = 1000 meters (m)\t1 month (mo) = 30 days (days)
1 inch (in) = 2.54 centimeters (cm)\t1 year (yr) = 365 days (days)
1 foot (ft) = 0.3048 meters (m)
1 mile (mi) = 1.60934 kilometers (km)

Explanation:

Step1: Convert yards to kilometers

Since 1 yard = 3 feet and 1 foot = 0.3048 meters and 1 kilometer = 1000 meters, then 1 yard = 3×0.3048 = 0.9144 meters = 0.0009144 kilometers. So 8 yards = 8×0.0009144 = 0.0073152 kilometers.

Step2: Convert days to months

We know that 1 month = 30 days. The object moves in 9.5 days, and we want to find the speed per month.

Step3: Calculate the speed in km per month

The speed $v$ is given by the formula $v=\frac{d}{t}$. Here, $d$ is the distance in kilometers and $t$ is the time in months. The distance $d = 0.0073152$ kilometers for 9.5 days. Let $x$ be the distance in kilometers per month. We set up a proportion: $\frac{0.0073152}{9.5}=\frac{x}{30}$. Cross - multiplying gives $9.5x=0.0073152\times30$. Then $x=\frac{0.0073152\times30}{9.5}=\frac{0.219456}{9.5}\approx0.02$.

Answer:

0.02