Math Problems?

Question

A right circular cylinder is 188.5 square inches ,if its height is 7 inches,what is it radius?
A = 2pi r h+2pi r^2
188.5=6.28(7)r+6.28r^2
6.28r^2+43.96r-188.5=0
I dont know to how to go from there

A bathroom tub will fill in 15 minutes with both faucets open and the stopper in place. With both faucets closed and the stopper removed,the tub will empty in 20 minutes. How long will it take for the tub to fill if both faucets are open and the stopper is removed?
x=faucets y=stopper ,x+y=15,15-x-y=20
do i set it like this to a system of equations?

An air rescue plane averages 300 miles per hour in still air. It carries enough fuel for 5 hours of flying time. If,upon take off,it encounters a wind of 30 miles per hour and the direction of the airplace is with the wind in one direction and against it in the other,how far can it fly and return safely? Assume that the wind remains constant.
300/(x-30) + 300/(x-30) = 5
[300(x-30)+300(x+30)] /(x-30)(x+30) =5
600x/x^2-900 =5 ?

Answer 1

For the first problem, use the quadratic formula (see source cited below if you need to review this formula). The formula will give you one positive solution (just a bit above 3) and a negative solution (which of course you must discard; you can't have a negative radius).

For the second problem:

The faucets put water in at a rate of 1 tubful/15 minutes
The drain lets water out at a rate of 1 tubful/20 minutes

Let t be the time in minutes to fill the tub. Then

1 tubful = (1 tubful/15 min)(t min) - (1 tubful/20 min)(t min)

The units check, so we can drop them and write this more briefly as

1 = t/15 - t/20

I'll let you solve this. You should get t = 60

For the third problem, you need the relation

distance = rate × time in the form

time = distance/rate

For this problem, the total time of 5 hr is spent partly flying against the wind, and partly flying with the wind. So the equation will take the form

total time = (time flying against the wind) + (time flying with the wind)

which, using time = distance/rate for each time on the right side, is

total time = distance/(speed against the wind) + distance/(speed with the wind)

For the time during which the plane flies against the wind, its speed relative to the ground is 300 - 30 = 270mph; and when flying with the wind, its ground speed is 300 + 30 = 330 mph.

Let D be the distance (in miles) for either leg of the two-way trip. Then

5 hr = (D miles)/(270 mph) + (D miles)/(330 mph)

The units check (hr on both sides of the equation), so let's drop them and write this as

5 = D/270 + D/330

Solve for D. You should get D = 742.5 miles