Question

The time t required to drive certain distance varies inversely with the speed r. It takes 2 hours to drive the distance at 40 miles per hour,how long will it take to drive the same distance at 45 miles per hour?

Answer 1

`(16)/(9)` hours

Explanation:

Whenever 2 quantities (suppose a and b) are inversely proportional to each other, we can write an proportionality equation (with k as proportional constant) as:

`a=(k)/(b)`

Since, here t is INVERSELY PROPORTIONAL to r, we can say:

`t=(k)/(r)`

Firstly, we have t = 2 hour and r = 40 mph, so we find k:

`t=(k)/(r)\\2=(k)/(40)\\k=2*40\\k=80`

Now, secondly, we have r = 45 and k = 80, we need to find t:

`t=(80)/(45)\\t=(16)/(9)`

So, it would take
`(16)/(9)` hours