The time, t, required to drive a fixed distance varies inversely as the speed, r. it takes 9 hr at a speed of 14 km/h to drive a fixed distance. how long will it take to drive the same distance at a speed of 23 km/h?

Time t=5.5 hours

Explanation:

The first we need to do is to define what speed is:  

Physics state that speed is the relation or the measuring of how much space or distance is traveled by an object in a given time

The less time the object takes to move, the faster it is. It indicates then that speed will be a relation between distance and time

To find your answer we will use the previous definition, where t is the time is takes, x is the distance it moves and r is the speed it uses to move.  

In this case:

For the first scenario we have an object that takes a time t of 9hr with a 14km/h speed r to drive a distance x. We will find how much x is to proceed with the second scenario, this way:

The distance it drives is x=126km

For the second scenario we´re asked to find the time t it takes to drive the same 126km but with a speed r of 23km/h. We will find how much t is this way:

Then the new time it takes to drive the same distance with a higher speed will be t=5.5 hours

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