While tutoring for the PSAT’s I can across this question
Jill can shovel a drive way in 20 Min and Mike can do the same driveway in 50 min
If they work together how long will it take them to shovel the driveway?
My question is How do you solve this using math you would find in pre-calc or earlier?
2006-11-07 03:25:47 · 7 answers · asked by John Z 1 in Science & Mathematics ➔ Mathematics
You have to think of the portion of a job that they would complete in an hour.
Jill would clear the 3 driveways in an hour. (20 min = 1/3 --> reciprocal = 3)
Mike would clear 6/5 driveways in an hour. (50 min = 5/6 --> reciprocal = 6/5)
So together they would clear 4 1/5 driveways in an hour (21/5)
If they could complete 4 1/5 driveways in one hour, 1 driveway would take the reciprocal or 5/21 of an hour. In other words, working together they would take 5/21 of an hour.
5/21 * 60 = 300/21 = 100/7 or 14 2/7 minutes.
The answer is:
14.285714 minutes, which is a little more than 14 minutes 17+ seconds
This answer makes sense because it should be faster than either of them working separately.
2006-11-07 03:30:59 · answer #1 · answered by Puzzling 7 · 0⤊ 0⤋
Since Jill can shovel a driveway in 20 mins, her rate of shovelling is 1 driveway / 20 minutes.
Since Mike can shovel a driveway in 50 minutes, his rate of shovelling is 1 driveway / 50 minutes.
Working together, their total rate is the sum of their individual rates: J + M = 1/20 + 1/50 = 5 / 100 + 2 / 100 = 7 driveways / 100 minutes
Dividing the numerator and denominator by 7 gives you 1 driveway / 14.3 minutes.
It takes 14.3 minutes for both of them working together to shovel a driveway.
2006-11-07 03:37:49 · answer #2 · answered by Clueless 4 · 0⤊ 0⤋
Without using algebra, figure the least common multiple of 50 and 20 which is 100. Jill could do 5 driveways in 100 min and Mike could do 2 driveways in 100 min. So together they do 7 driveways in 100 min. Divide 100 by 7 to see how long it takes them to do one driveway. 100/7 is about 14.28 min.
2006-11-07 04:02:02 · answer #3 · answered by hayharbr 7 · 1⤊ 0⤋
1 driveway in 20 minutes = 1/20
1 driveway in 50 minutes = 1/50
add them together because they are working together
1/20 + 1/50 = 1/n (1 driveway in n minutes)
5/100 + 2/100 = 1/n
7/100 = 1/n
7n = 100
n = 100/7
n = 14.29 minutes
2006-11-07 03:33:38 · answer #4 · answered by SPB 6 · 0⤊ 0⤋
Jills 1 min jopb=1/20
Mikes 1 min job=1/50
together their 1 min job=1/20+1/50
=7/100
so they will take 100/7 min to
complete it together
the answeris 14 2/7 min
2006-11-07 03:37:53 · answer #5 · answered by raj 7 · 0⤊ 0⤋
there are 2 people so you add the minutes which is 70 and divide that by the 2 and you get 35 min.
2006-11-07 03:33:14 · answer #6 · answered by ruth4526 7 · 0⤊ 1⤋
do not understand.
2006-11-07 03:27:43 · answer #7 · answered by eli_prkns 2 · 0⤊ 0⤋