Question 1174166: A biology teacher drives from Naperville over the Cleveland to visit her sister. During the trip there, she travels the first half of the time at 65 km/hr and the second half the time at 95 km/hr. When she comes back, she drives the first half the distance at 65 km/hr and the second half of the distance at 95 km/hr. What is her average speed coming back from Cleveland?
I am confused how to calculate this. I thought it might just be the average of the two speeds but that is not the correct answer. Also, I tried to set up an equation, but solving this did not give me the right answer. The equation I thought might work (wrong answer of 78.6 km) was D/160 + D(1/260 + 1/380), and then divided 1 by 0.0127 (sum of all the D terms). Any help would be greatly appreciated. Thank you.
Answer by ikleyn(52879)   (Show Source):
You can put this solution on YOUR website! .
A biology teacher drives from Naperville over the Cleveland to visit her sister.
During the trip there, she travels the first half of the time at 65 km/hr and the second half the time at 95 km/hr.
When she comes back, she drives the first half the distance at 65 km/hr and the second half of the distance at 95 km/hr.
What is her average speed coming back from Cleveland?
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Solution
Let " t " be her total time driving from N to C.
Then the total distance from N to C is d = 0.5t*65 + 0.5t*95 = 0.5t*(65+95) = 0.5t*160 = 80t kilometers.
Half the distance is 40t kilometers.
When driving back (from C to N), the total driving time is T =  +  hours. (1)
The average speed driving back is the total distance 80t divided by the total time of the formula (1), i.e.
 =  =  = 77.1875 kilometers per hour. ANSWER
Solved.
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Is everything clear to you in my solution ?
When you complete read it, do not forget to post your "THANKS" to me for my teaching.
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For the problem, it does not matter, who is the driver: "biology teacher", or carpenter, or sales manager, or astronaut,
or vice-president, or anybody else.
Therefore, naming his (or her) specialty is IRRELEVANT to the problem.
I know that 80% of problems in US Math textbooks are formulated this way.
It is NOT an argument that they all are correct; they all are WRONG.
They teach young students to think incorrectly, and, in addition, they treat the students inadequately . . .
As a result, when such a student sees the words "vice-president" instead of "biology teacher",
he (or she) thinks that it is another problem . . .
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