Question

The time t required to drive a certain distance varies inversely with the speed r. If it takes 2 hours to drive the distance at 30 miles per hour, how long will it take to drive the same distance at 50 miles per hour?

Answer 1

Inverse variation means \[y = \frac{k}{x}\]or\{xy = k\]You have time \(t\) varying inversely with speed \(s\), and a constant distance \(d\).

\[d = st\]\[d = 30*2\]\[d = 50*t\]What is the value of \(t\) necessary for that to produce the same value of \(d\) in the two equations?