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?
+129850
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
+129850 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
+129850 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
