Two ships start out from the same point. The first ship plans to sail northeast on a constant heading, going three mi east for each four mi north, at a speed of 30mi/h. The second ship plans to sail due north, and then sail due east. At what speed must the second ship sail in order to guarantee that they will rendezous(meet) ? If they plan to rendezous in 6h, how long should the second ship sail north before it heads east?
Ok so;should i solve this by a rate times time equals distance? Or actually plot the slopes; :( i dont know how to do this. Not sure how to graph the problem >:O. help?
2007-09-28 14:49:15 · 3 answers · asked by Kate! 3 in Science & Mathematics ➔ Mathematics
This is a really good question to start your thinking juices.
Try to picture the courses of both ships when they meet.
It will be a triangle; what else do we know about it's size?
The sides will be proportional to the direction travelled.
The eastern track will be 3x, the northern track will be 4x.
It will be a right-angle triangle; so by Pythagorus:
The route of the first ship will be 5x in length.
At 30 mph for 6 hours, that will be 360 miles.
If 5x = 360, then x = 72.
The second ship must travel 7x miles in 6 hours.
That's 7(72)/6 or 84 mph.
The second ship must change direction at 4x miles.
4(72)/84 = 3.43 hours, meet in 3(72)/84 = 2.57 hours.
2007-09-28 15:14:56 · answer #1 · answered by Robert S 7 · 0⤊ 0⤋
Answer: The second ship go with the same speed as the first one is...
See.. if both the ships start out from the same point and at the same time.. they sh'd have same speed to meet again... if not they will never meet... why because , one of them is going north and then east... but the second one will also travel the same distance but it keeps changing the directions as per the rules of 4mi north and 3 mi east...but in total both the ships travel the same distance.. so, for the ships to meet... they sh'd have the same travel speed .. see the plot below...
for meeting after 6 hrs, the second ship will travel a distance of = 6 x 30 = 180 miles, but for every 7 miles it completes a step of 4 mi north and 3 mi of east... that means...
to travel 180 miles it will cover = 180/7 = 25 steps + 5 miles travel
i.e. 25 x 4 mi towards north + 4 mi north and in east wards it will travel 25 x 3 mi + 1 mi
thus the 2nd ship sh'd travel = 25x4 + 4 = 104 mi north
2007-09-28 15:05:08 · answer #2 · answered by Metallurgist 2 · 0⤊ 1⤋
Draw it. This problem can be hard to understand and solve without a diagram.
2007-09-28 14:56:27 · answer #3 · answered by Anonymous · 1⤊ 0⤋