John and Lucy are standing at point A. Both of them starts walking in opposite direction at the same time. John is walking at 4 miles/hour while Lucy is walking at the speed of 3 miles/hour. How much time will it take John to travel double the distance Lucy traveled in the same amount of time.

How to solve this type of speed/dist problem???? No ans is available.


Thanks in advance..

Punzo

Punzo,

I always use a rate chart to solve rate problems. So, for this problem, the step-by-step process would be as follows:

1) Set up the Rate Chart
2) Fill in Rate information
3) Fill in Time information (often the variable [i]t[/i])
4) Multiply across to fill in Distance/Work information.
5) Derive an equation and solve.

.....R..*..T..=..D
J....4......t......4t
L....3......t......3t

Because John's distance will then be double Lucy's distance, we can derive the equation 4t = 2(3t). If we simplify, we then get 4t = 6t. Subtracting 4t from both sides results in 0 = 2t, and then, 0 = t.

Now this does not seem to be a very sensible answer. And the reason for this is that John will NEVER have traveled double the distance of Lucy if they are walking for the same amount of time. Why? Because their rates are in the ratio of 4:3. So their distances will be in the same ratio.

Consider this table:

Time..John's Dist..Lucy's Dist
..1..........4..............3
..2..........8..............6
..3.........12.............9
..4.........16.............12
..5.........20.............15

As you can see, the ratio always remains 4:3 so long as their times are the same. In order for John to have traveled double Lucy's distance, the ratio would have to be 2:1.

I hope that helps!

- Dan P