A ship left at 9:00 am going 10 miles per hour on a course. Another ship left at noon on the same course going 15 miles per hour. At what time did the second ship overtake the first ship?
Well write it out, let 1 represent 10:00 in the x coordinant's position, and let y be the miles out on the course the ship is.
Ship 1
10:00 11:00 12:00 1:00 2:00
(1,10);(2,20);(3,30);(4,40);(5,50);
3:00 4:00 5:00 6:00 7:00
(6,60);(7,70);(8,80);(9,90);(10,100)
Ship 2
1:00 2:00 3:00 4:00 5:00
(4,15);(5,30);(6,45);(7,60);(8,75);
6:00 7:00
(9,90);(10,105)
There is probably an easier way to find it out, though.
Let t hours be the time since noon, when the second ship passes the first.
distance covered by slower ship = 10(t+3) mile
distance covered by faster ship = 15 t
but at that moment they both had gone the same distance, so ....
15t = 10(t+3)
15t = 10t + 30
5t=30
t = 6
so the second ship passed the first 6 hours past noon or 6:00 pm
check:
slower ship sailed for 9 hours at 10 mph = 90 miles
faster ship sailed for 6 hours at 15 mph = 90 miles
Answer is correct.
To find out at what time the second ship overtakes the first ship, we need to determine the time difference between when the first ship started and when the second ship started, as well as calculate when the two ships are at the same position.
First, let's calculate the time difference between when the first ship started (9:00 am) and when the second ship started (noon). To do this, we subtract the starting time of the first ship from the starting time of the second ship: noon - 9:00 am = 3 hours.
Now we need to determine the position at which the two ships meet. The first ship has been traveling for 3 hours at a speed of 10 miles per hour, which gives us a distance of 3 hours * 10 miles per hour = 30 miles. This means that the first ship is 30 miles ahead of the second ship when the second ship starts.
Since the second ship is traveling at 15 miles per hour and needs to catch up to the first ship by 30 miles, we can calculate the time it will take for the second ship to cover this distance. The time it takes is given by distance / speed = 30 miles / 15 miles per hour = 2 hours.
Therefore, if the second ship started at noon and it would take 2 hours to catch up to the first ship, the second ship will overtake the first ship at noon + 2 hours = 2:00 pm.