Question 556337
You have to be careful with problems like this one. You can't just say that in order to average 50 mph you can do 1 lap at 30 mph and the second lap at 70 mph because you know that the average of 30 and 70 is (30 + 70)/2 = 100/2 = 50 mph.
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In order to average 50 mph for the two laps of 1 mile each (total distance of 2 miles) you need to determine how much time it would take to cover the total 2 mile distance. Use the equation:
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D = R*T
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where D represents the total distance, R is the rate in mph, and T is the time in hours. Substitute 2 miles for the total distance and 50 mph for the average rate you want to get. Then solve for T as follows:
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2 = 50*T
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Divide both sides by 50 and you get:
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2/50 = T
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Note that on the left side the numerator and the denominator are both divisible by 2. So the fraction on the left side reduces to 1/25 and the equation for the time you have to complete the two laps is 1/25 of an hour.
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Now you can look at how long it took to complete the first lap at a rate of 30 mph. The total distance was 1 mile and the rate was 30 mph. The time it took to make this single lap can be found from the same equation. Start with:
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D = R*T
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Substitute 1 mile for D and 30 mph for R. Then solve for T as below:
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1 = 30*T
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Divide both sides by 30 and you have:
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T = 1/30
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So you complete the first lap in 1/30 hour.
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Now since to average 50 mph you must complete the two laps in 1/25 hour and you used 1/30 of an hour to complete this first lap, you can subtract 1/30 from 1/25 and determine the time you have left to complete the second lap.
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So find:
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1/25 - 1/30 =?
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Let's convert these two to decimals to make it easier to find the difference between them. When you divide 25 into 1 you get 0.0400000 hr and when you divide 30 into 1 you get 0.0333333 hr. So you now can find the time to complete the second lap by subtracting as follows:
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0.0400000 - 0.0333333 = 0.0066666 hr
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So the second 1 mile lap must be completed in  a time of 0.0066666 hr. Substitute these two values into the equation:
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D = R*T
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and you get:
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1 = R*0.0066666
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You can solve for the rate in mph by dividing both sides of this equation by 0.0066666 to get:
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1/0.0066666 = R
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Doing the division on the left side results in:
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150 mph = R
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Surprise! You have to drive the second 1-mile lap at 150 mph in order to average 50 mph for the two laps. 
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Hope this helps you to understand the problem a little better. And you can see why I warned you not to simply figure that covering 1 lap at 30 mph and the second lap at 70 mph would give you an average speed of 50 mph.
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