1) I drove to my parents' house at 60 miles per hour. If I had driven 50 miles an hour instead, then I would have gotten there 40 minutes later. How many miles did I drive?

2) Anabel's horse runs 24 miles per hour. Jackie's horse runs 28 miles per hour. Both horses stand at the starting line of a straight 2-mile track, and Jackie's horse starts running 30 seconds after Anabel's. How many miles from the starting line does Jackie's horse catch up to Anabel's?

3) Fake gold bricks are made by covering concrete cubes with gold paint, so the cost of the paint is proportional to their surface area while the cost of the concrete is proportional to their volume. If a 1 inch cube costs $1.30 to make while a 2 inch cube costs $6.80, then how much would a 3 inch cube cost?

Guest Oct 27, 2017

#1**+1 **

1) I drove to my parents' house at 60 miles per hour. If I had driven 50 miles an hour instead, then I would have gotten there 40 minutes later. How many miles did I drive?

Distance / Rate = Time

Let the time be in hours...40 minutes = 2/3 hrs.......so, equating times

D / 50 = D / 60 + 2/3

D / 50 = [3D + 120 ] / 180 cross-multiply

180 D = 50 [ 3D + 120 ] simplify

180 D = 150 D + 6000 subtract 150 D from both sides

30D = 6000 divide both sides by 30

D = 200 miles

CPhill
Oct 27, 2017

#2**+1 **

2) Anabel's horse runs 24 miles per hour. Jackie's horse runs 28 miles per hour. Both horses stand at the starting line of a straight 2-mile track, and Jackie's horse starts running 30 seconds after Anabel's. How many miles from the starting line does Jackie's horse catch up to Anabel's?

Note.....the number of 30 second intervals in one hour = 120

At 24 mph, Anabel's horse runs 24 / 120 = 1/5 mile in 30 seconds

So...her horse has a 1/5 mile head start

And Anabel]s horse runs 24/60 = 2/5 mile in a minute = 6/15 miles per minute

And Jackie's horse runs 28/60 = 7/15 mile in a minute

So....Jackie's horse closes the distance between them at 1/15 miles per minute

So......the time it take's Jackie's horse to catch Anabel's is

( 7/15 - 6/15) M = 1/5

1/15 M = 1/5 multiply both sides by 15

M = 3 minutes......and in 3 minutes, Jackie's horse runs 3 (7/15) = 7/5 miles

CPhill
Oct 27, 2017

#4**+1 **

3) Fake gold bricks are made by covering concrete cubes with gold paint, so the cost of the paint is proportional to their surface area while the cost of the concrete is proportional to their volume. If a 1 inch cube costs $1.30 to make while a 2 inch cube costs $6.80, then how much would a 3 inch cube cost?

Let the cost of paint per square inch = P

Let the cost of concrete per cubic inch = C

Surface area of 1 inch cube = 6 in^2 and of a 2 inch cube = 24 in^2

Volume of 1 inch cube = 1 in^3 and of a 2 inch cube = 8 in^3

So...we have the following system

6P + 1C = 1.30 ⇒ -24P - 4C = - 5.20 (1)

24P + 8C = 6.80 (2)

Add (1) to (2) and we have

4C = 1.60 divide both sides by 4

C = .40

And

6P + 1(.40) = 1.30

6P = .90 divide both sides by 6

P = .15

And the surface area of a 3 inch cube = 54 in^2

And the volume is 27 in^3

So.....the cost of a 3 inch cube is

54 (.15) + 27 (.40) = $ 18.90

CPhill
Oct 27, 2017