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Abiana wants to get to the opposite corner of a rectangular park that is $3/4$ miles wide and $1$ mile long. If she rides her scooter, it only takes her 8 minutes to travel 1 mile, but she has to go around the park. If she walks, it takes her 20 minutes to travel 1 mile, but she can cut directly across the grass. Which mode of transportation is faster, assuming she travels at a constant speed?

 Aug 27, 2023
 #1
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Distance by scooter =  3/4 +1 =  1.75 miles

Time to travel =  1.75 miles * 8 min/mile   =    14 min

 

If she goes straigt across we can use the P Theorem to  find the distance because it will be the hypotenuse of a  right triangle with legs of 1, 3/4  miles

D =  sqrt  [ 1^2  + (3/4)^2 ]  =   sqrt [ 1 + 9/16 ] = sqrt [  25/16 ]  = 5/4 miles

Time to  travel by foot =  (5/4)miles * 20 min / mile  = 25 min

 

Faster by scooter  !!!!

 

cool cool cool

 Aug 27, 2023

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