To minimize the time it takes to get to the store, you need to find the point on the shore that is closest to the island. This will involve drawing a straight line from the island to the shore and finding the point on the shore where this line intersects.
Since you can row at 4 mph and walk at 5 mph, you should first row to the point on the shore closest to the island, and then walk the rest of the way to the store.
Using the Pythagorean theorem, we can calculate the distance from the island to the shore at the closest point:
a^2 + b^2 = c^2
6^2 + x^2 = 7^2
36 + x^2 = 49
x^2 = 13
x ≈ 3.6 miles
So, you should land approximately 3.6 miles down the beach from the convenience store in order to minimize the time it takes to get the tortilla chips.
You’re sunbathing on the island shown on the map below. The island is six miles from shore at
the closest point, and the nearest store is a convenience store seven miles down the beach. If
you can row at 4 miles an hour, and you can walk at 5 miles an hour, where should you land to
get a bag of tortilla chips in the least possible time? (Ignore tides, currents, and sharks. No fair
renting a helicopter.)
1 answer