Science:Math Exam Resources/Courses/MATH110/April 2014/Question 06
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q2 (a) • Q2 (b) • Q2 (c) • Q3 (a) • Q3 (b) • Q3 (c) • Q3 (d) • Q3 (e) • Q3 (f) • Q3 (g) • Q4 • Q5 • Q6 • Q7 (a) • Q7 (b) • Q8 (a) • Q8 (b) • Q9 (a) • Q9 (b) • Q9 (c) •
Question 06 

At noon, ship is kilometres west of ship . Ship is sailing east at kilometres per hour and ship is sailing north at kilometres per hour. How fast is the distance between the ships changing at 4:00 p. m. on the same day? (You should indicate in your answer if the distance between the ships is increasing or decreasing.) 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Draw a diagram to illustrate the setting, and label the diagram with variables that might be useful later. 
Hint 2 

What is the rate that we are trying to find? 
Hint 3 

Relating the rates directly is difficult. Try to relate the variables first. 
Hint 4 

Differentiate with respect to the correct variable to obtain a relation between the rates that we want. 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. This is a related rates problem. So we go about it using the standard related rates approach.
