.Jack, Daug and Ann, 3 Children had running race while returning from school. Mom asked who won the race. Then Jack replied, "I want tell u. I will give u clue.
* When Ann takes 28 steps. Daug take 24 steps, meantime I take 21 steps. Jack explained that his 6 steps equals Daug's 7 steps & Ann's 8 steps. Who won the Race?
pls explain with answers
2006-07-31 15:22:05 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Let Jack's step be worth 1 foot (it really doesn't matter what unit you use)
Then Doug's step is worth 6/7 feet
and Anne's step is worth 6/8 feet
Then Ann goes 28 steps * 6/8 feet/step = 21 feet
Doug goes 24 steps * 6/7 feet/step =~ 20.5714 feet
and Jack goes 21 steps * 1 foot / step = 21 feet
so Jack and Ann tied, Doug lost
2006-07-31 15:33:11 · answer #1 · answered by bogusman82 5 · 0⤊ 0⤋
First we need to determine how much each step is worth:
We generate a large enough number (in units) that has factors for all three.
6 x 7 x 8 = 336 units
Then we calculate what each step is in terms of units.
Jack 1 step = 336/6 = 56 units
Daug 1 step = 336/7 = 48 units
Ann 1 step = 336/8 = 42 units
Finally,
Distance covered:
Jack: 21 x 56 = 1176 units
Doug: 24 x 48 = 1152 units
Ann: 28 x 42 = 1176 units
Both Jack and Ann are tied at first place having covered the same distance.
2006-07-31 22:41:16 · answer #2 · answered by ideaquest 7 · 0⤊ 0⤋
Jack won the race because has a longer leg than the others; by the time jack takes 6th steps (his last step, Daug will have one more step to take and Ann will still have 3 more steps to take after Jack has finished the race. it needs thinking. i hope i am right.
2006-07-31 22:33:53 · answer #3 · answered by labo 2 · 0⤊ 0⤋
Ann and Jack tied, because the ratio of her number of steps to Jack's is 28/21 which is 4/3, and the ratio of her length of steps to Jack's is 6/8, which means they will cover exactly the same distance in the same length of time== a ratio of 1:1. Doug only takes 21 steps to Ann's 28, a ratio of 3/4, and his steps are 8/7 the length of hers. 3/4 X 8/7 = 24/28, or 6/7, which means he can cover only 6/7 the distance in the same length of time as the other two. He is the loser, and, worse, alone in his defeat!
2006-07-31 23:34:46 · answer #4 · answered by John (Thurb) McVey 4 · 0⤊ 0⤋
(6)JS = (7)DS = (8)AS
If JS = 1 meter, then
28 Ann steps = 6/8 * 28 = 21
24 Daug steps = 6/7 * 24 = 20.5714
21 Jack steps = 6/6 * 21 = 21
Ann and Jack tied.
2006-07-31 22:34:21 · answer #5 · answered by Michael M 6 · 0⤊ 0⤋
28/8=3.5
24/7=3.4
21/6=3.5
these are their respective running rate with respect to there steps...
therefore they just got home almost at the same time...
ann and jack arrived first at the same tie while daug although lost from them both,also managed to catch up in no time at all...
2006-07-31 22:33:22 · answer #6 · answered by angel r 2 · 0⤊ 0⤋
I am guessing Anna
2006-07-31 22:27:01 · answer #7 · answered by IxLovexThisxBoy 2 · 0⤊ 0⤋
duag.
2006-07-31 22:35:49 · answer #8 · answered by rick 2 · 0⤊ 0⤋