help on word problems?

Question

completely forgot how to do these =[

can anyone help?

alice cycles to carla's house at 12 mi/h and returns by car at 36 mi/h. if the round trip is 1 hour, how far from carla does alice live?

i got 24 minutes..but i just guessed in how to set up the equation

and also

find four consecutive whole numbers such that the sum of the squares of the first and third is 2 less than 6 times the fourth.

yeahh..i tried this a couple of times and ended up with 12, 13, 14, and 15.
i couldn't really figure out how to set up this one either. if you could help it would be great. thanks!

Answer 1

distance = rate times time, so time = distance divided by rate.

if d = the distance to Carla's house, d/12 + d/36 = 1

get a common denominator and solve

Answer 2

#1.
No! The answer is Carla lives 9 miles away. And it took Alice 45 minutes to cycle to Carla's house. Here's why.

Let x be the time in minutes it took Alice to get to Carla's. Then because she was traveling three times as fast on her return, the amount of time it took to return was (x / 3) minutes. The sum of the times was 60 minutes. So, we can set up this equation:

x + x / 3 = 60

Mutiply by 3 to clear fractions.

3x + x = 180 ----> 4x = 180 ----> x = 45.

So it took Alice 45 minutes to cycle to Carla's.

Converting minutes to hours, we get 45 minutes = (3/4) hours.

(3/4) hr (12 mi / hr) = (36 / 4) mi = 9 mi.

So Carla lives 9 miles from Alice.

#2.
x = 1st, x +1 = 2nd, x + 2 = 3rd, x + 3 = 4th.

Set up your equation like this:

x² + (x + 2)² = 6 (x + 3) - 2
x² + x² + 4x + 4 = 6x +18 - 2
2x² + 4x + 4 = 6x + 16
2x² - 2x - 12 = 0
(2x² - 2x - 12 ) / 2 = 0 / 2
x² - x - 6 = 0
(x + 2)(x - 3) = 0
x = -2 or x = 3

Since whole numbers are considered to be the normal counting numbers, plus 0, we discard -2. Then our numbers become 3, 4, 5, 6.

Check: (3)² + (5)² = 34 = 6 (6) - 2 = 34.

By the way, even though we are forced to discard -2, it still works. Given x = -2, the others are -1, 0 and 1.

(-2)² + (0)² = 4 = 6 (1) - 2 = 4.

( [:¬] )

Answer 3

For the second one, your numbers don't quite work. Let x be the first number. Then you need:

6*(x+3) - (x^2 + (x+2)^2) = 2.

Solving this equation out, you get that x = -2 and x = 3 both work.

Answer 4

1)36/12=3
2)4321