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Quant Review 2019 - PS question 4 - not able to post the diagram :/
A certain harbor has docking stations along its west
and south docks, as shown in the figure; any two
adjacent docking stations are separated by a uniform
distance d. A certain boat left the west dock from
docking station #2 and moved in a straight line
diagonally until it reached the south dock. If the boat
was at one time directly east of docking station #4 and
directly north of docking station #7, at which docking
station on the south dock did the boat arrive?
How can this question be solved using equation of a line?
A certain harbor has docking stations along its west
and south docks, as shown in the figure; any two
adjacent docking stations are separated by a uniform
distance d. A certain boat left the west dock from
docking station #2 and moved in a straight line
diagonally until it reached the south dock. If the boat
was at one time directly east of docking station #4 and
directly north of docking station #7, at which docking
station on the south dock did the boat arrive?
How can this question be solved using equation of a line?
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15 Apr 2020, 04:24
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rkaur897
Hello rkaur897,
Yes, why not!
In fact this question has to be solved using the equation of a straight line. More specifically, when you use the “Intercept Form” of the equation of the line, solving this question becomes extremely simple.
All that you have to do is to replace the co-ordinates of 5 with the origin and the respective numbers on the horizontal axis with 1, 2, 3 etc. When you do this, you will see that the y-intercept of the line is 3 – the boat starts from station #2 and that is 3 units from the origin on the y-axis.
The question asks us to find the x-intercept of the line i.e. the station on the south dock at which it arrived.
The intercept form of the equation of a straight line is \(\frac{x}{a}\) +\( \frac{y}{b}\) = 1, where a is the x-intercept and b is the y-intercept.
Since b = 3, \(\frac{x }{ a}\) + \(\frac{y }{ 3}\) = 1 represents the equation of the line which represents the route that the boat is taking to reach a station on the south dock, having started from station 2 on the east dock.
The boat was directly east of station#4 and north of station#7 i.e 1 on the y-axis and 2 on the x -axis. This means, the line passed through (2,1). Substituting these values in the equation of the straight line, we have,
\(\frac{2}{a}\) + \(\frac{1}{3}\) = 1. Solving, we get a = 3 which essentially means station #8.
I hope this answers your question about how the equation of a line can be used to solve this question ?
Hope that helps!
15 Apr 2020, 09:29
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rkaur897
This question is discussed here: a-certain-harbor-has-docking-stations-along-its-west-and-south-docks-271978.html In case of questions please post there. Hope it helps.
Also, please read carefully and follow our posting rules: rules-for-posting-please-read-this-before-posting-133935.html Thank you.
THIS TOPIC IS LOCKED AND ARCHIVED.
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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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Thank you for understanding, and happy exploring!
