Two Algebra 1 questions..?

Question

These kind always seem to confuse me =/
And whoever answers this, can you please explain it? I'm not just trying to get answers, I want to know how to actually do it =]

1. A freight train leaves a station traveling 60 miles per hour. Thirty minutes later a passenger train leaves the station in the same direction on a parallel track at a speed of 72 miles per hour. How long will it take the passenger train to catch the freight train?

2. A container company wants to make a cylindrical can with a volume of 1188 cubic inches. The formula V=piR²h represents the volume of a cylinder. In this formula, V represents the volume, r represents the radius of the cylinder's base, and h represents the height of the cylinder. Solve for h. What height should the company make the can if the radius of the base must be 6 inches?

(Yeah I'm not sure how to make a 'pi' symbol so i just wrote it in)

Thanks!

Answer 1

I never can remember how to answer the first question

but the second one i can!

first make the equation solve for h

V=piR(2)h

divide piR(2)

h=V/piR(2)

plug in the numbers

h=1188/pi*36

h=10.5

Answer 2

1. For question 1, the first thing to determine is how far the first train has gone when the second train leaves. Since 60 mph is one mile per minute, after 30 minutes it will have traveled 30 miles.

The next thing to think about is this: the second train is starting 30 miles behind. And the second train is traveling 12 miles per hour faster. So every hour, the second train makes up 12 of those 30 headstart miles. How many hours until the headstart is zero? Can you turn the word problem into an equation?

2. There are two steps to solving problem 2. Step 1 is simple: plug in all the known values into the equation. So:
V = πR²h
becomes
1188 = π6²h --- because we substitute 1188 for V, and 6 for R.
Step 2: we have to re-write the equation so that the unknown (h) is alone on one side of the equation. Start by dividing both sides by π:
1188 / π = 6² h
Now divide both sides by 36, or 6²:
1188 / 36π = h
... and finally, just evaluate everything on the left-hand side, and you've got it.

Answer 3

If the time is t, in that time, the first train will travel 60t

Whilst the second 72 (t-0.5)

Put these equal 60 t = 72(t-0.5)
12t = 36
t = 3

They give you V, reorder to the form h =
they now tell you h, inserting gives the answer

Answer 4

sqrt(2x+3)=sqrt(6x-one million) 2x +3 = 6x-one million 4 = 4x x = one million verify sqrt(2*one million +3) = sqrt(6*one million -one million) sqrt5 = sqrt5 assessments A sqrt(b^4/24) = 4 2sqrt(b^4/6) = 4 sqrt(b^4/6) = 2 b^2sqrt6 = 2 b^2 = 2/sqrt6 = sqrt4/sqrt6 = sqrt(2/3) b = +/- 4th root of (2/3) so not one of the above. are you optimistic the challenge is sturdy? if the 24 is replaced to twenty-5, that's what happens sqrt(b^4/25) = 4 b^2/5 = 4 b^2 = 20 b = +/- 2sqrt5 D