Efficiently Solve Difficult Math Problems

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The discussion centers on solving a math problem involving average speed over different segments of a trip. The user initially struggled with calculating the average speed for the last 20 miles and found their approach time-consuming. They calculated the time for the first 30 miles as 3/4 hour and the last 20 miles as 13/36 hour. A suggested method involves determining the total trip time and comparing it to a calculated value using long division. The conversation emphasizes finding efficient strategies to tackle complex math problems.
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Homework Statement


What is the best way to do this problem? It looked easy but when I the solution just wasn't clicking for me. I tried to calculated the average speed of the last 20 miles explicitly and it took me a really long time and I had to crudely approximate the answer...I am pretty sure there is a simple way to do this.


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Hint: Figure out the time it takes for the total trip and each segment.
 
Doc Al said:
Hint: Figure out the time it takes for the total trip and each segment.

That's pretty much what I did. The first 30 miles take 3/4 hr and the last 20 miles take 13/36 hr. So then I just need to figure out whether 20*36/13 is greater than 45 by long division, right?
 
ehrenfest said:
That's pretty much what I did. The first 30 miles take 3/4 hr and the last 20 miles take 13/36 hr. So then I just need to figure out whether 20*36/13 is greater than 45 by long division, right?

That's correct.
 

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