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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
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 #1
avatar+78590 
+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    

 

 

 

cool cool cool

CPhill  Oct 27, 2017
 #3
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Let the time that took you to drive at 60 mph=T

Distance = Time x Speed

60T = 50[T + 2/3], Solve for T 

T = 3 1/3 hours.

Distance =3 1/3 x 60 mph=200 miles you drove.

Guest Oct 27, 2017
 #2
avatar+78590 
+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

 

 

cool cool cool

CPhill  Oct 27, 2017
 #4
avatar+78590 
+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

 

 

cool cool cool

CPhill  Oct 27, 2017

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