SOLUTION: The amount of time for a trip varies inversely as the speed traveled. A car reached its destination in 9 hours traveling at 60 mph. What must its speed be to get there in only 8 ho

Algebra ->  Functions -> SOLUTION: The amount of time for a trip varies inversely as the speed traveled. A car reached its destination in 9 hours traveling at 60 mph. What must its speed be to get there in only 8 ho      Log On


   

Question 175478: The amount of time for a trip varies inversely as the speed traveled. A car reached its destination in 9 hours traveling at 60 mph. What must its speed be to get there in only 8 hours?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let t=time and r=rate/speed

"The amount of time for a trip varies inversely as the speed traveled" translates to t=k%2Fr


Now find the value of k:


t=k%2Fr Start with the given equation.


9=k%2F60 Plug in t=9 and r=60


9%2A60=k Multiply both sides by 60 to isolate k.


540=k Multiply


So the value of k is k=540


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So the equation becomes {{t=540/r}}} after plugging in k=540


Now let's answer the question: "What must its speed be to get there in only 8 hours?"

t=540%2Fr Start with the given equation.


8=540%2Fr Plug in t=8


8r=540 Multiply both sides by r.


r=%28540%29%2F%288%29 Divide both sides by 8 to isolate r.


r=135%2F2 Reduce.


r=67.5 Divide.


So the speed would need to be 67.5 mph in order to get there in 8 hrs