You've got a job at a company and you will be traveling to a conference with accommodation. You leave home on monday at 07:15 and arrive at 11:07. The next day you drive exactly the same route back. There is less traffic so you start at 8:32 and arrive at 11:01. Show that there is a point on that route you were at, at the exact same time the two days.

musicintimeln

musicintimeln

Answered question

2022-08-11

You've got a job at a company and you will be traveling to a conference with accommodation. You leave home on monday at 07:15 and arrive at 11:07. The next day you drive exactly the same route back. There is less traffic so you start at 8:32 and arrive at 11:01. Show that there is a point on that route you were at, at the exact same time the two days.

Okay, so that is my question. Does anyone know how to go about this one? I think I need to use the intermediate value theorem, but I'm not sure how to! Thanks in advance for tips/solutions.

Answer & Explanation

vibrerentb

vibrerentb

Beginner2022-08-12Added 21 answers

Extend your drive back: get in the care at 7:15 and wait until 8:32 to start moving; when you arrive at 11:01, sit in the car until 11:07.
The fraction of the way you've gone along the route on the first day is a function
f : [ 7 : 15 , 11 : 07 ] [ 0 , 1 ]
with f ( 7 : 15 ) = 0 and f ( 11 : 07 ) = 1.
Similarly, there's a function g indicating the fraction for the return trip, but for g, we have g ( 7 : 15 ) = 1 and g ( 11 : 07 ) = 0.
Let h = g f. Then h is continuous, h ( 7 : 15 ) > 0, and h ( 11 : 07 ) < 0. Now you should be able to apply the IVT.

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