Therefore, they meet after x = 6 hours from the start of the journey.

During 6 hours, Alice must have traveled a distance of 60 ´ 6 = 360 miles.

Hence they must meet at a point which is 360 miles from A.

Example A boat goes downstream in 1 hours and returns in hours. If the stream is flowing at 3 miles per hour, what is the speed of the boat in still water ?

Let r be the speed of the boat in still water.

downstream                        upstream

And the speed of the stream is 3 miles per hour.

The rate of the boat downstream = (r + 3) miles per hour and

its rate upstream = (r - 3) miles per hour.

Using distance = rate ´ time

Therefore, downstream = (r +3) ´ 1 = ( r + 3) miles

and upstream = (r - 3) ´ = ( r - 3) miles.

Since these two distances are the same,

we have r + 3 = (r - 3)

2 r + 6 = 3 r - 9

6 + 9 = 3 r - 2 r

15 = r

Therefore, the speed of the boat in still water is 15 miles per hour.

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Index

9.1 - Definition and Solving Techniques
9.2 - Use of Simultaneous Linear Equations

Chapter 1