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 #1
avatar+1281 
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I drove to the beach at a rate of 40 miles per hour.  If I had driven at a rate of 50 miles per hour instead, then I would have arrived 45 minutes later.  How many miles did I drive?  

 

You mean 45 minutes earlier.  Obviously, if you drive faster, you get there faster.  

 

This problem makes use of

the following relationship:                   Distance = Velocity x Time 

 

                                                           D  =  V • T  

 

case 1                                                 D  =  (40) • (T)  

 

case 2                                                 D  =  (50) • (T – 45)  

 

Since the Distance, D, is the  

same for both cases, let's set       

the "V•T"s equal to each other.             (50)(T – 45)  =  (40)(T)  

 

                                                               50T – 2250  =  40T  

 

Subtract 40T from both sides                  10T – 2250  =  0  

 

Add 2250 to both sides                                       10T  =  2250  

 

Divide both sides by 10                                           T  =  225   (this is time in minutes)  

 

Divide minutes by 60 to get hours          225 minutes  =  3.75 hours  

 

Plug this T back into original equation                     D  =  (40 mi/hr) • (3.75 hr)  =  150 miles  

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18 Jun 2023
 #1
avatar+1281 
+1

 

One ordered pair (a,b) satisfies the two equations ab^4 = 48 and ab = 72. What is the value of b in this ordered pair?  

 

 

To find b, consider                                                  ab4  =  48  

 

We will divide both sides by ab.  

 

Since ab=72, we will divide the left side  

by "ab" and the right side by its equal 72.  

                                                                              ab4         48  

                                                                             ——   =   ——  

                                                                              ab           72  

Note that ab4 = (ab) * (b3)  

 

Cancel ab out of the left side.  

Reduce 48/72 on the right side.  

                                                                               b3           2  

                                                                             ——   =   ——  

                                                                                1            3  

 

 

                                                                                 b   =   cube root of (2 / 3)  

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17 Jun 2023