Problem Solving

Peter and Jacob are at the northwest corner of a field, which is a rectangle 300 ft long and 160 ft wide. Peter walks in a straight line directly to the southeast corner of the field. If Jacob walks 180 ft down the west side of the field and then walks in a straight line directly to the southeast corner of the field, what is the difference in the distance traveled by the two?

A) 20
B) 40
C) 80
D) 120
E) 140

The OA is B.

I don't have clear this PS question. I appreciate if any expert explains it to me. Thank you so much.

Hello AAPL.

Let's take a look at your question.

The following image shows how the walked.


Now, we can see that the distance walked by Peter is: $$\sqrt{160^2+300^2}=\sqrt{25600+90000}=\sqrt{115600}=340\ ft$$

On the other hand, the distance walked by Jacob is 180 ft + TF. And we can calculate TF as follows: $$TF=\sqrt{120^2+160^2}=\sqrt{14400+25600}=\sqrt{40000}=200\ ft$$ This implies that the distance walked by Jacob is 180+200 = 380 ft.

Finally, the difference between the distance walked by Peter and Jacob is: 380-340 = 40 ft.

Therefore, the correct answer is the option B.

I hope this answer may help you.

Feel free to ask me again if you have a doubt.

Regards.