Question

Two fishing boats depart a harbor at the same time, one traveling east, the other south. the eastbound boat travels at a speed 1 mi/h faster than the southbound boat. after 5 h the boats are 25 mi apart. find the speed of the southbound boat.

Answer 1

The speed of the southbound boat is 4 miles per hour.

Step-by-step explanation:

To find the speed of the southbound boat, let's consider the distance traveled by each boat after 5 hours. Since the eastbound boat travels at a speed 1 mile per hour faster than the southbound boat, let's assume the speed of the southbound boat as x miles per hour. Therefore, the speed of the eastbound boat will be (x + 1) miles per hour.

Distance traveled by the southbound boat = speed x time = x * 5 = 5x miles

Distance traveled by the eastbound boat = speed x time = (x + 1) * 5 = 5x + 5 miles

According to the problem, after 5 hours, the boats are 25 miles apart. So, the equation becomes: 5x + 5 - 5x = 25. Solving this equation gives x = 4.

Therefore, the speed of the southbound boat is 4 miles per hour.

Answer 2

they are travelling at right angles to each other.
At any given instant they form a right triangle with their starting point
South bound = x [mi/h]
East bound = x+1 [mi/h]
after five hours they will be
d=5x
and
d=5(x+1)
miles away from the starting point
(5x)^2+(5(x+1))^2=625
25x^2+(5x+5)^2=625
25x^2+25x^2+50x+25=625
50x^2+50x-600=0
x^2+ x - 12=0
(x+4)(x-3)=0
take the postive value
x= 3 mph the speed of south bound
4mph east bound