A ship leaves a port at 12:00 Noon and sails East at speed of 10 miles/hour. Another ship leaves
the same port at 1:00 PM and sails North at a speed of 20 miles/hour. At what time are the two
ships going to be 50 miles apart from each other? (Hint: Distance = Speed * Time)
Just plug in your distance formula and solve for t when d=50. At t hours past noon,
d = √((10t)^2 + (20(t-1))^2)
d = 10√(5t^2-8t+4)
when d=50,
5t^2-8t+4 = 25
5t^2-8t-21 = 0
(5t+7)(t-3) = 0
we want t>0, so at t=3 (3:00 pm) the ships are 50 miles apart
Note that the negative value of t means that if the ships had been sailing on the same courses, rather than just starting out, they would also have been 50 miles apart at t=-7/5, or at 10:36 am. Of course, that might have been awkward, coming at the port from the land side!
I did not anderstand the answer
the paths of the ships form two legs of a right triangle, where the distance between the ships is the hypotenuse. As usual, draw a diagram.
Now, the hypotenuse of a triangle with legs a and b is
d = √(a^2+b^2)
The length of the legs is the distance traveled by the ships, which is each ship's speed times the # hours spent sailing.
The 10 km/hr ship has been going for t hours, but the other ship waited an hour before starting out, so its sailing time is only t-1 hours.
To find out at what time the two ships will be 50 miles apart from each other, we can use the distance formula, which is Distance = Speed * Time.
Let's first calculate the time it will take for the first ship to sail 50 miles. We know that the speed of the first ship is 10 miles/hour.
So, Time = Distance / Speed
Time = 50 miles / 10 miles/hour
Time = 5 hours
Now, let's calculate the time it will take for the second ship to sail 50 miles. The speed of the second ship is 20 miles/hour.
Time = Distance / Speed
Time = 50 miles / 20 miles/hour
Time = 2.5 hours
Now, we need to consider the time difference between the two ships. The second ship leaves one hour later than the first ship, which means it has to travel for one hour less to reach the same distance.
So, the total time for the second ship to reach 50 miles apart from the first ship would be 2.5 hours - 1 hour = 1.5 hours.
To determine the time at which the two ships are 50 miles apart, we need to add the time it took for the first ship to the time it took for the second ship. Since the second ship left the port at 1:00 PM, we add the time it took for the first ship (5 hours) to 1:00 PM.
Therefore, the two ships will be 50 miles apart at 1:00 PM + 5 hours = 6:00 PM.