Question 160404: A car travels a 1 mile track at an average speed of 30 miles per hour. At what average speed must the car travel the next mile so that the average speed for the 2 miles is 60 miles per hour?
How do you set this problem up to solve it? My teacher said that it is not possible to average 60 miles per hour, but I do not understand why or even how to try to set this problem up. This problem comes from a handout and not a text book, and we are charged with finding the formula and are given the answer. If the car was going 30mph for 1 mile, then if the car traveled 90mph for the second mile, than wouldn't the 2 speeds added together and divided by 2 average out to be 60mph? Please help! I really hate word problems, and it has been 22 years since I have had to do them!
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Basically, it is IMPOSSIBLE.
.
You will be applying the "distance" formula:
d = rt
where
d is distance
r is rate or speed
t is time
.
In order to average 60 mph over 2 miles, the "time" needed to do this is:
d = rt
t = d/r
t = 2/60 = 1/30 hour
.
The time the car took in the first mile (doing 30 mph) is:
d = rt
t = d/r
t = 1/30 = 1/30 hour
.
Notice, there is NO time left to compensate on the second mile.
.
Conclusion:
Since, the car already consumed ALL the time, no matter how fast he goes in the second mile he cannot achieve the AVERAGE rate of 60 mph.
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