A coast guard helicopter receives a distress signal from a boat. the units (15,80) (55,38)represent miles. to the nearest minute, how long will it take the helicopter to reach the boat if the helicopter travels at an average speed of 75 miles per hour?
(15 , 80) , (55 , 38).
d^2 = (55 - 15)^2 + (38 - 80)^2,
d^2 = (40)^2 + (-42)^2,
d^2 = 1600 + 1764,
d^2 = 3364,
d = 58 Miles.
t = 58 mi / 75 mi / h = 0.77 h = 46 min
To find the time it will take for the coast guard helicopter to reach the boat, we can use the distance formula and divide it by the average speed of the helicopter.
First, let's calculate the distance between the helicopter and the boat using the given coordinates (15,80) and (55,38). We can use the distance formula, which is the square root of the sum of the squared differences in x-coordinates and y-coordinates.
Let's calculate the difference in x-coordinates: 55 - 15 = 40.
And the difference in y-coordinates: 38 - 80 = -42.
Now, let's square these differences: (40^2) + (-42^2) = 1600 + 1764 = 3364.
Taking the square root of 3364, we get √3364 ≈ 58.01 miles (rounded to two decimal places).
Now, we can calculate the time it will take to travel this distance at an average speed of 75 miles per hour:
Time = Distance / Speed
Time = 58.01 miles / 75 miles per hour ≈ 0.77 hours.
To convert this into minutes, multiply the decimal part by 60:
0.77 hours * 60 minutes per hour ≈ 46.2 minutes (rounded to the nearest minute).
Therefore, it will take the coast guard helicopter approximately 46 minutes to reach the boat.