The research vessel needs to travel 30 miles per hour to be in the same location as Shark 1 or 34 miles per hour to be in the same location as Shark 2 at 7 p.m.
Students may use a variety of strategies and solution paths to determine how far each shark is from the boat at 2 p.m. and how fast the vessel needs to travel to reach the sharks at 7 p.m.
The solution below is based on each shark’s given location and the time they travel in 5 hours. Their location at 7 p.m. (10 hours) could also be used instead and is just double the distances for 5 hours.
Shark 1 traveled 75 miles in 5 hours.
Shark 2 traveled 85 miles in 5 hours.
Distance from the Boat to each Shark’s Location
Apply the Pythagorean Theorem
Shark 1
a2 + b2 = c2
602 + 452 = c2
3,600 + 2,025 = c2
5,625 = c2
c = `sf(sqrt(5,625))` = 75 miles
Shark 2
a2 + b2 = c2
362 + 772 = c2
1,296 + 5,929 = c2
7,225 = c2
c = `sf(sqrt(7,225))` = 85 miles
Area Model of the Pythagorean Theorem
Speed of the Research Vessel
The sharks will travel for another 5 hours at their current rate. This means the vessel needs to travel twice as fast as the sharks to catch up to them.
OR
Shark 1
75 miles ÷ 5 hours = 15 miles per hour
15 mph x 10 hours = 150 miles
Vessel speed: 150 miles ÷ 5 hours = 30 miles per hour
Shark 2
85 miles ÷ 5 hours = 17 miles per hour
17 mph x 10 hours = 170 miles
Vessel speed: 170 miles ÷ 5 hours = 34 miles per hour
Surround and Subtract Area
Shark 1
Shark 2
Area of Large Square:
105 • 105 = 11,025 square miles
Area of Each Triangle:
(45 • 60) ÷ 2 = 1,350 square miles
Area of all 4 Triangles:
1,350 • 4 = 5,400 square miles
Area of Hypotenuse Square (shaded area):
11,025 – 5,400 = 5,625 square miles
Side Length of Hypotenuse Square (c) = `sqrt(5,625)` = 75 miles
Area of Large Square:
113 • 113=12,769 square miles
Area of Each Triangle:
(36 • 77) ÷ 2 = 1,386 square miles
Area of all 4 Triangles:
1,386 • 4 = 5,544 square miles
Area of Hypotenuse Square (shaded area)
12,769 – 5544 = 7,225 square miles
Side Length of Hypotenuse Square (c) = `sqrt(7,225)` = 85 miles
MP.1
Make sense of problems and persevere in solving them.