Can u solve this SAT math q?

Discus: What Are My Chances?: December 2002 Archive: Can u solve this SAT math q?
 By 660M; i hate the hard qs! on Saturday, December 28, 2002 - 09:32 pm: Edit

Ok, im prepping for the SAT on my own and the 10 REAL SATs dont give explanations on how they found answers. Im a sped, so can u guys help?

here's two:
1) It took juanita a total of 10 hrs to hike from the base of the mountain to the top and back down again by the same path. If while hiking she averaged 2km/hr going up and 3 km/hr coming down, HOW MANY KM was it from the base of the mt. to the top?

2) One side of a triangle has a length 6 and a second side 7. Which of the following could be the AREA??
I. 13
II.21
III.24

OK, so i know the first one deals with average speed/rate, but not much else.

For the second, i know its based on the triangle inequality theorem (3rd side must >diff. <sum of two sides) but what do i do with that? HELP! I know this is a zinch for you 800 Math ppl.

 By 800 in math on Saturday, December 28, 2002 - 09:37 pm: Edit

1)Let x=the time needed to go up, then
2x=3(10-x)
x=6
so the distance from the base to the top is: 2*6=12(km)

2)if this is a right triangle and those two sides are perpendicular, then the area is 6*7/2=21.So *II* is the answer.

 By 660M on Saturday, December 28, 2002 - 09:39 pm: Edit

THANKS!! i love smart people!

 By 660M on Saturday, December 28, 2002 - 09:40 pm: Edit

Note: these are the ones from the FIRST practice tests..expect a LOT more in the coming days/wks

 By Adam on Saturday, December 28, 2002 - 09:41 pm: Edit

First one: 24 km
It has to be the same distance up and down
D = ST 6 X 2 = 12 and 3 X 4 = 12. add them together, you get 24.

2nd one: It could be I and II. Just find the maximum area - which would use the two given sides as the non-hypotenuse of a right-triangle, and that is 21. Anything else smaller can be made with different angles.

 By person on Saturday, December 28, 2002 - 09:42 pm: Edit

the answer to number 1 is 12 km.

heres why:

x = length

x/2 + x/3 = 10 hours

(5/6)(x) = 10

x = 12 km

there is no way for me to explain number 2. You just have to visualize or draw a picture which is impossible for me to do.

 By me on Saturday, December 28, 2002 - 09:43 pm: Edit

1) 12km
otw up: 12km @ 2km/hr = 6 hr
otw down: 12km @ 3km/hr = 4 hr
6 hr + 4 hr = 10 hr

2) A = bh/2
plugging in 6 as base we get
A = 3h
now plugging in 13, 21, and 24 you see that it is possible to attain a height of 13/3 and 7. 8 is not possible because the second side has a length of 7 and no matter which way you swing it it will never be 8 from the base. plugging in 7 as the base will also work for this, but is more tedious.

 By adam on Saturday, December 28, 2002 - 09:43 pm: Edit

And Im an idiot.

 By 660M on Saturday, December 28, 2002 - 09:44 pm: Edit

o wait, i just checked the book...#2 is actually 21 and 13.(I and II)..i dont think you can just assume its a right triangle..does anybody else have a clue about the 2nd one? (the first is right tho,thanks)

 By 800 in math on Saturday, December 28, 2002 - 09:45 pm: Edit

I agree with you on the 2nd one. So the following item should be added

IV. both I and II

 By 800 in math on Saturday, December 28, 2002 - 09:48 pm: Edit

SAT I math problems can be pretty tricky sometimes :P

 By Pat57575 (Pat57575) on Saturday, December 28, 2002 - 09:58 pm: Edit

yet you managed to get an 800... how many did you miss...0, 1, 2?

 By 800m on Saturday, December 28, 2002 - 10:04 pm: Edit

I think I missed 1(probably that was the experimental part though), while I messed up 4 of them on my first attempt and only got a 760.

 By Pat57575 (Pat57575) on Saturday, December 28, 2002 - 10:09 pm: Edit

4?! Once I missed 2 and got 740!

 By 800m on Saturday, December 28, 2002 - 10:13 pm: Edit

you were unlucky then...