Question 1174166
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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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<B>Solution</B>


<pre>
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 = {{{40t/65}}} + {{{40t/95}}}  hours.       (1)


The average speed driving back is the total distance  80t  divided by the total time of the formula (1), i.e.


    {{{V[average]}}} = {{{80t/((40t)/65 + (40t)/95)}}} = {{{2/(1/65+1/95)}}} = 77.1875 kilometers per hour.    <U>ANSWER</U>
</pre>

Solved.


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Is everything clear to you in my solution ?


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For the problem, &nbsp;it does not matter, &nbsp;who is the driver: &nbsp;"biology teacher", &nbsp;or carpenter, &nbsp;or sales manager, &nbsp;or astronaut, 
or vice-president, &nbsp;or anybody else.


Therefore, &nbsp;naming his &nbsp;(or her) &nbsp;specialty is &nbsp;IRRELEVANT &nbsp;to the problem.


I know that &nbsp;80% &nbsp;of problems in &nbsp;US &nbsp;Math textbooks are formulated this way.


It is &nbsp;NOT &nbsp;an argument that they all are correct; &nbsp;they all are WRONG.


They teach young students to think incorrectly,   &nbsp;&nbsp;and, &nbsp;in addition, &nbsp;they treat the students inadequately . . . 



As a result, &nbsp;when such a student sees the words &nbsp;"vice-president" &nbsp;instead of &nbsp;"biology teacher", 
he &nbsp;(or she) &nbsp;thinks that it is another problem . . .