x = hours walked level; so 6-x = hours up and down
Miles walked
= 4x + 3[2(6-x)/3] + 6(6-x)/3
= 4x + 12 - 2x + 12 - 2x
= 24
Here is a problem to try and solve:
Jack and Jill walked along a level road, up the hill, back (along the same path) down te hill, and back along the same level road to home. They started out at 3pm and arrived home at 9pm. Their speed was four miles an hour on the level, three miles an hour uphill, and six miles an hour down hill.
a.) How far did they walk in all (level, up, down, level)?
b.) You can't figure out from the given information exactly when they reached the top of the hill. How closely can you approximate when they arrived there? (e.g. can you give an interval of an hour containing the time they arrived at the top? An interval of a half hour?)
Hello, matgrl!
Here's another approach to part (a).
Jack and Jill walked along a level road and up a hill.
Then walked back along the same path:
. . down the hill and along the same level road to home.
They started out at 3 pm and arrived home at 9 pm.
Their speed was 4 mph on the level, 3 mph uphill, and 6 mph downhill.
a.) How far did they walk in all (level, up, down, level)?Code:* * * y * * * * * * * x
They walked miles (level) at 4 mph.
. . This took: . hours.
Then they walked miles (uphill) at 3 mph.
. . This took: . hours.
They walked miles (downhill) at 6 mph.
. . This took: . hours.
Then they walked miles (level) at 4 mph.
. . This took: . hours.
The entire trip took 6 hours: .
Multiply by 12: .
. .
They walked 12 miles one way.
The entire walk was 24 miles.
First do you see that Soroban carefully stated what his variables meant: "x is miles walked on the level", "y is miles walked down hill". He then has an equation that has four parts- timed walked on the level toward the mountain, time walked uphill, time walked down hill, and time walked on the level away from the mountain, using x in both "level" walks, and y in both uphill and downhill walks. The whole route is "level toward mountain" (x), "uphill" (y), "downhill" (y again), and "level away from mountain" (x again). The whole route is x+ y+ x+ y= 2x+ 2y= 2(x+ y) so that x+ y is the first "level toward mountain" plus "uphill" (which is the same as "downhill" plus "level away from mountain". We know that x+ y is one way rather that roundtrip because we know what "x" and "y" separately meant.
(Yes, times/speeds for descent are included in the equation but the distance (y) is the same both ways.)
As I recall, in the Reverand Dodgson's (AKA Lewis Carroll) original puzzle, it was a knight and squire. Why the change to "Jack" and "Jill"?