Efficiently Solve Difficult Math Problems

[ehrenfest]

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.

Homework Equations

The Attempt at a Solution

 

[Doc Al]

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

 

[ehrenfest]

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?

 

[konthelion]

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.