QR Question From Practise OAT

[goodie]

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I just finished going through the sample OAT posted on the ada website and for some reason cant seem to figure out the following QR question:

At 7:00 a.m. a student leaves his home in his automobile to drive to school 28 miles away. He averages 50 mph until 7:30 a.m. when his car breaks down. The student has to walk and run the rest of the way. If he wants to arrive at school at 8:00 a.m. how fast, in mph, must he travel on foot.

Answer: 3

I figure speed = distance/time so for the first half hour the student covers 25 miles (50mph/0.5h) so they have 3 miles left to go in the last half hour 3miles*0.5h = 1. 5 mph?

Where am I going wrong?? 😕

 

[Artemis2]

The answer is 6.

you are going wrong on the last step. It is miles per hour so you should calculate it like this:
3 miles/0.5 hours = 6 mph

 

[goodie]

Oh wow, I knew I was overlooking something silly! Thanks Artemis!

One other question (and any that are similar) that always stump me is:

The value of cos (π/3) equals the value of
A. – cos (2π/3).
B. cos (2π/3).
C. cos (6π/3).
D. – cos (5π/3).
E. cos (4π/3)

I've got my sin, cos and tan values memorized for 30 (pi/6), 30 (pi/4), 60 (pi/3) and 90 (pi/2) .. I'm just not sure how to apply it to these types of questions. Any helpful explanations would be great!!

 

[Artemis2]

First off I think it is probably just a typo, but pi/4 = 45.
i don't think the values are needed in this question.
basically what you are looking for is the complement negative number that will give you one.

cos (pi/3) = 0.5
-cos (2pi/3) = 0.5

I think of it like a circle you are trying to complete by going opposite directions around it.

Sorry if that is confusing, it is the only way I know how to explain it.