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 #1
avatar+818 
+1

 

Will and Grace are canoeing on a lake.  Will rows at 50 meters per minute and Grace rows at 20 meters per minute. Will starts rowing at 2 p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at 2 p.m. If they always row directly towards each other, and the lake is 3800 meters across from the west side of the lake to the east side, at what time will the two meet?  

 

Will's rate is 50 m/min.  

Grace's rate is 20 m/min.  

 

They're rowing toward each other,  

so their rate of closure is 70 m/min.  

 

The lake is 3800 meters across.  

 

The time it will take them to meet is given by  

                                                                                    Distance  

                                                                            T  =  –––––––  

                                                                                       Rate  

 

                                                                                    3800 m  

                                                                            T  =  –––––––  

                                                                                    70 m/min  

 

The time it takes them to meet                             T  =  54.29 min  

 

Note that (0.29 min • 60 sec/min)  =  17 seconds

 

The time on the clock is                                             2:54:17 pm 

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16.06.2023
 #1
avatar+818 
+1

 

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 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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15.06.2023