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River crossing - solve the problem

Last updated almost 5 years ago

8 questions

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Question 1

1.

What is the length of AC in terms of x?

Using the formula for time taken for travel at a constant speed,
 write down and expressionin terms of x for:

Question 2

2.

the time taken to swim from A to C.

Question 3

3.

the time taken to run from C to D.

Question 4

4.

Hence write down an expression for the time taken, T, to travel from A to D in terms of x.

You want to minimise this expression (find the minimum time taken).

Question 5

5.

Find

Question 6

6.

Now solve
to determine the value of x that minimises the time taken.

Question 7

7.

How do you know this is a valid value?

Question 8

8.

For this value of x, find the minimum time possible and descibe the route.