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?

icecreamchocolate Aug 27, 2023

#1**+1 **

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 !!!!

CPhill Aug 27, 2023