Working alone it would take laura 45 minutes to mow the lawn kelly would take 1 hour 15 minutes if they work together the girls believe it will take 1 hour to mow the lawn which is the best described of the solution

31.5 minutes only

Inverse proportion

Step-by-step explanation:

It takes 45 minutes for Laura to mow the lawn.

For Kelly it takes 1 hour 45 minutes or 60+45 = 105 minutes

In one minute Laura can mow 1/45 of the lawn.

Similarly in one minute Kelly can mow 1/105 of the lawn

Together in one minute they can mow the sum

=

Take lcd for 45 and 105 and make them equivalent fractions with same denominator

LCD of 45 and 105 is 15(3) (7) = 315

In other words it would take 63/2 = 31.5 minutes only to lawn if they work together.

The situation here is the problem on inverse proportion.  If no of people increase, work time would decrease.

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.