Question

John’s age is three times that of Alan’s. Ralph’s age is twice that of Alan’s.
What is the ratio of John’s age to Ralph’s?

6:1
2:3
3:2
1:6

Answer 1

@jim_thompson5910

Answer 2

What is the ratio of John's age to Alan's age?

Answer 3

They don't give anyone's age. That's the confusing part.

Answer 4

I would say 3:2

Answer 5

It doesn't matter, ratios don't require specific numbers, they simply give relations between two numbers. If box A is twice as big as box B, then the ratio of their sizes is 2:1. Can you now tell me what the ratio of John's age to Alan's age is?

Answer 6

3:1

Answer 7

@Tom982 It doesn't tell me. Everything I posted above is all the information they give me.

Answer 8

I think you're misunderstanding me. You're given that "John’s age is three times that of Alan’s", so what is the ratio between the two ages?

Answer 9

@tom982 Wouldn't it be 3:1? Since John's age is 3 time Alan's 1? :/

Answer 10

Exactly!

Answer 11

Now what is the ratio of Ralph to Alan?

Answer 12

Would it be 2:1?

Answer 13

@tom982

Answer 14

Or would it be 2:3? :/

Answer 15

Exactly, so J:A = 3:1, and R:A = 2:1. So J:R = 3:2. You could look at this another way, if it helps you understand. We know J=3A and R=2A, now find J in terms of R and write it as a ratio:
A=0.5R
J=3A=3(0.5R)=1.5R
2J=3R which is equivalent to saying J:R = 3:2.

Answer 16

Thanks Tom I understand now! :)

Answer 17

No problem! Glad you understand.

Answer 18

tom you are great at explaining things! (I am too but I lack the patience)

Answer 19

@tom982
A neutron star has a density of about 5.9 10 17 kg/m3.
What would be the approximate mass of a 1-centimeter cube (a cube 1 cm on all sides)?
5.9 10^14 kg (1300 trillion pounds)
5.9 10^8 kg (1.3 billion pounds)
5.9 10^17 kg (1.3 quadrillion pounds)
5.9 10^11 kg (1.3 trillion pounds)

In a recent census, New York City had a population of 8,336,697 people, and an area of 302.64 square miles, while London had a population of 3,792,621, and an area of 469 square miles. (No choices)
What are the population densities (to the nearest person) of the two cities?
New York:
London:

A road map has a scale of 10 miles per inch. The length of the straight-line road on the map between two cities is 6 inches. If the road between the cities has a speed limit of 30 mph, about how long should it take to drive from one city to the next?
2 hours
4 hours
1 hour
3 hours

A scale model of an office building is 3' x 2' x 5' (length, width, height). If the actual building has a length of 45 feet, what is the volume of the actual building?
81,000 cubic feet
102,150 cubic feet
101,250 cubic feet
30,000 cubic feet

Answer 20

Okay let's work through these part by part, starting with the neutron star.

Answer 21

OK!

Answer 22

We know the weight is 5.91017 kgm^{-3} and we want the weight of a 1cm cube, so we can either convert the weight into kgcm^-3 or convert the 1cm cube into m^3. Take your pick!

Answer 23

Convert the 1cm cube to m^3

Answer 24

Okay, so what's 1cm^3 in m^3?

Answer 25

Sorry I'm not too sure how to convert it. :(

Answer 26

Okay, no worries. What's 1cm in m?

Answer 27

Would it be 1.0 × 10-6 m^3

Answer 28

0.01

Answer 29

0.01 is correct :) So there's 0.01cm in a m, and 0.01^2 cm^2 in m^2, so how many cm^3 are in a m^3?

Answer 30

umm... 1,000,000cm3? Sorry if it's wrong, i'm really bad at math.

Answer 31

No you're not, that last question couldn't be more wrong if I tried, sorry about that. You're perfectly right, but what I meant to ask was how many m^3 in cm^3 which is 1/1000000=0.0000001. So we know our 1cm^3 cube is 0.0000001m^3, and we know a neutron star weighs 5.91017 kg per cubic metre, so what's the weight of our cube?

Answer 32

1,300 trillion pounds? The first answer choice?

Answer 33

I have one too many zeroes in my previous post, it should be: 0.000001.

Answer 34

And is your question meant to say 5.9x10^17? Because all I see is 5.9 10 17.

Answer 35

0.000001*5.9x10^17=5.9x10^11

Answer 36

Oh so it would be the last one. for the first one. :)

Answer 37

Exactly

Answer 38

Now for the second one!

Answer 39

Divide the number of people by the number of square miles to find the people per square mile for each of them (round accordingly) :)

Answer 40

So NYC: 27546.5800952
London: 8086.6119403

Answer 41

@tom982

Answer 42

Rounded it would be
NYC: 27,546.58
London: 8,086.61

Right?

Answer 43

Close, can you have 0.58 of a person?

Answer 44

No. So would I just remove the decimal entirely?

Answer 45

Yeah, well, round it: "What are the population densities (to the nearest person) of the two cities?"

Answer 46

@tom982 I already rounded from hundredths place and that's how I got those results. If I remove the decimal it would be 27,546 and 8,086. Is that correct?

Answer 47

You're not rounding from hundredths, you're rounding to the nearest whole number.

Answer 48

NYC: 27,547
London: 8,087

Answer 49

Yep, spot on

Answer 50

Yay! Third problem. :)

Answer 51

10 miles per inch. So 6 inches is how many miles? Then at 30mph, how long would it take to drive that distance?

Answer 52

@tom982 1 hour?

Answer 53

No, we know 6 inches is 60 miles and at 30 miles per hour, this would take 2 hours.

Answer 54

I'm sorry it should be 2 hours, right?

Every 10 miles you're going an inch, so in 6 inches you're going 60 miles. You then do 30/60 which is 2.

Answer 55

Yeah, but your last fraction is upside down :)

Answer 56

Oh lol, thanks!