SOLUTION: THE TIME IT TAKES A CAR TO TRAVEL A FIXED DISTANCE VARIES INVERSELY WITH THE RATE AT WHICH IT TRAVELS. IT TAKES THE CAR 4 HOURS TO TRAVEL A FIXED DISTANCE WHEN IT TRAVELS AT A RATE

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Question 72971: THE TIME IT TAKES A CAR TO TRAVEL A FIXED DISTANCE VARIES INVERSELY WITH THE RATE AT WHICH IT TRAVELS. IT TAKES THE CAR 4 HOURS TO TRAVEL A FIXED DISTANCE WHEN IT TRAVELS AT A RATE OF 50 MILES PER HOUR. HOW FAST DOES THE CAR HAVE TO TRAVEL TO COVER THE SAME DISTANCE IN 2.5 HOURS?

WHOEVER ANSWERS, THANK YOU GREATLY FOR YOUR HELP!!!!!!!!!!!!!!!!!!!!!!
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
The distance equation is normally written as:
.
D+=+R%2AT
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where D stands for distance, R stands for the rate or speed, and T stands for the time.
You use this equation lots of times. Think, "If I go at 50 miles per hour (rate) and I
drive for 3 hours (time), how far do I travel?" You do this in your head ... 50 miles every
hour then in 3 hours you go 150 miles.
.
In this problem we are going to be using this equation to calculate the rate. Think, "If I
go 150 miles and I drive for 3 hours, how many miles per hour did I go?" This time you can see that
to go 150 miles in 3 hours you have to average 50 miles per hour as your rate. That's pretty
basically what we are going to be doing.
.
Now back to the problem. The first part of the problem tells you that you drive at 50 mph
for 4 hours. How far did you go?
.
Use the equation:
.
D+=+R%2AT and substitute 50 for R and 4 for T to get:
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D+=+50%2A4+=+200 miles.
.
So the distance you want to travel is 200 miles.
.
Now the problem asks you how fast you have to go (rate) if you want to cover the same distance
in 2.5 hours.
.
Return to the equation:
.
D+=+R%2AT and substitute 200 miles for D and 2.5 hours for T to get:
.
200+=+R+%2A+2.5
.
You can find R by dividing both sides by 2.5 and when you do you get:
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200%2F2.5+=+R+%2A+2.5%2F2.5
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This simplifies to:
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200%2F2.5+=+R%2Across%282.5%29%2Fcross%282.5%29+=+R
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You can divide 2.5 into 200 and find that the answer is 80. So the final answer is that
to go 200 miles in 2.5 hours you have to travel at a rate of 80 miles per hour.
.
Too fast for safety and wastes gas.
.
Hope this discussion helps you to understand the problem a little more.