Algebra help?

I'm not exactly sure what part of algebra this is classified as, but if you could read the problems and see if you have any help to offer that would be lovely. I do need help, not just answers, I'm taking a test on this tomorrow and knowing how to do the problems is a must. I've done similar ones before but my brain has died

1) A cabin cruiser travels 20 miles in the same time that a power boat travels 40 miles. The cruiser travels 5 mph slower than the power boat. Find the speed of each boat.

2) A train travels 40 mph faster than a car. If the train covers 160 miles in the same time that the cat covers 80 miles, what is the speed of the car?

3) When making a telephone call using a calling card, a call lasting 5 minutes cost $1.45. A call lasting 14 minutes cost $3.25. Let y be the cost of making a call lasting x minutes using a calling card. Write a linear equation that models the cost of making a call lasting x minutes.

x = PB's speed

CC
20 miles
Speed = x-5 mph
Total time (hrs) = 20 / (x-5)

PB
40 miles
Speed = x mph
Total time (hrs) = 40 / (x)

Now find X by making time = time

40/x = 20/(x-5)
20x = 40 (x-5)
20x = 40x - 200
200 = 20x
x = 10

PB = 10mph
CC = 10-5 = 5mph

Thank fk for that, was sat here scribbling it out and got that answer, only to think "nah, that seems far too obvious!"

Same as you. I was double checking or more too.

Have I ever told you I love you?
Thank you so much



It does! I swear some of these I'm like "It can't be that. Can it? Too easy... But wait, it makes sense. GAH"

I hate that I'm having problems with these because I'm usually really good at algebra. I think it's the word problems that are getting to me.

Train
v= (x+40) mph
distance = 160 mi
time = t

Car
v = x mph
d = 80 mi
time = t

v = d/t
t = dv = 160 mi / (x+40) mph = 80 mi / x
= 2 / (x+40) = 1 / x
= 2x = x+40
= x = 40 mph

Car's speed = 40 mph?

I'm hungry.
You should chekc the answers again.

This is the thing, on both those first two, it looks obvious that it's half/double just from looking at the question, then the scribbles say the same thing

I've got post-it notes everywhere atm

Mind you, it's 4.30am here and I wouldn't say I'm all that fresh

Pretty sure you're correct as that answer is one of the multiple choice answers.

And I'm starting to refresh my brain now, yayyy

I'll probably get smacked for this, but that's one fast cat. lol

Oh dear I've got scribbles on my paper and it has to be turned in, ugh. Erase erase erase.

It does seem simple but for the test I have to be able to write out all my work, and that's what I have problems with. My brain gets me the answer but not how it got that. And that's with a lot of algebra, not these seemingly obvious ones.

Thank you for pointing that out. I think I'll actually leave that, it's amusing

Call 1 = 5 min = $1.45
C2 = 14 min = $3.25

Linear y=mx+b
y =$, x = min

$1.45 = 5m + b
$3.25 = 14m + b

Subtract the two
-1.8 = -9 m
m= 0.2

y = 0.2x + b

Substitute into one linear eq to get b

$1.45 = 5m +b
1.45 = 5(0.2) + b
1.45-1= b
b = 0.45

NOW

y = 0.2x + 0.45

Ok, good, that's the answer I got but it seemed faaarrrrr too obvious.

Thanks everybody, for helping and giving me some good laughs