1) He worked 4 hours leaving 6 more hours for him.
rate for A alone 6 baker
rate for A & B together 4
1/a+1/b=1/x
1/6+1/b=1/4
1/b=1/4-1/6
1/b=6/24-4/24
1/b=2/24
1/b=1/12
b=12
rate for wife alone 12 hours for the remaining 6 hours
check
1/6+1/12=1/4
12/72+6/72=1/4
18/72=1/4
ok
codewa
But we want to know how long it would have taken her for the whole job not just part of it
he works twice as fast as she does so the job that takes him 10 hours alone would take her 20 hours alone.
2) jessica and cynthia work in a pet shop.
it takes jessica 6 hours to groom all the pets but cynthia needs 8 hours to groom them.
if jessica starts to groom 1 hour before cynthia joins, how long will it take them to finish?
:
let t = time it takes them to finish (C's working time)
then
t+1 = J's working time
let 1 = completed job (all pets groomed)
:
A shared work equation, each does a fraction of the job, the two fractions add up to 1
%28%28t%2B1%29%29%2F6 + t%2F8 = 1
Multiply by the least common multiple of 6 and 8, 24. cancel the denominators
4(t+1) + 3t = 24
4t + 4 + 3t = 24
4t + 3t = 24 - 4
7t = 20
t = 20/7
t = 26%2F7 hrs, which is: 2 + 6%2F7*60 = 2 hrs 51.43 min to finish the job
3) math club takes 40 minutes
science takes 50 minutes.
rate * time = quantity
quantity = 1 set up of the tables.
rate for math club is 1/40 of all the tables in 1 minute.
rate for science club is 1/50 of all the tables in 1 minute.
math club works for 10 minutes.
rate * time = quantity
1/40 * 10 = 10/40 = 1/4 of the tables are already set up by the math club.
there are 3/4 of the tables that still need to be set up.
rate * time = quantity
the rates of the math club and the science club are additive.
(1/40 + 1/50) * time = 3/4 of the tables that still need to be set up.
common denominator is 200.
(5/200 + 4/200) * time = 3/4.
9/200 * time = 3/4
time = 3/4 * 200/9 = 600 / 36 = 16 and 2/3 minutes.
total time required is 10 + 16 + 2/3 minutes = 26 + 2/3 minutes.
how to check.
10 minutes is used to do 1/4 of the tables.
16 + 2/3 minutes is used to do the remaining 3/4 of the tables.
combined rate of math and science club is 9/200 of the tables in 1 minute.
math club rate of 1/40 * 10 = 10/40 = 1/4 of the tables.
combine rate of 9/200 * (16 + 2/3) = 9/200 * 50/3 = 450/600 = 9/12 = 3/4 of the tables.
1/4 + 3/4 = 1 = all of the tables.
Answer:
Monique made an error when writing the factored expression.
Correct factored
expression=4x(1+4y)
Step-by-step explanation:
factoring the expression 4 x + 16 x y.
Factors of 4x: 1, 2, 4, x
Factors of 16xy: 1, 2, 4, 8, 16, x, y
GCF: 4x
Factored expression: 4 x (0 + 4 y)
Monique made an error when writing the factored expression.
The correct factored expression should be:
4x+16xy
=4x(1+4y)
Contrary to 4x(0+4y)
Correct factored
expression=4x(1+4y)
Answer:
1% of 4000 + 4% of B = 2% of (4000 + B)
40 + 0.04*B = 0.02( 4000 + B)
40 + 0.04* B = 80 + 0.02*B
40 + 0.04*B - 80 - 0.02B = 0
0.02*B - 40 = 0
0.02*B = 40
2B = 4000
B = 2000
Step-by-step explanation:
Answer:
-16
Step-by-step explanation:
So let’s solve for 7x. So 7x=34. So 7x-50 is 34-50 or -16
The next larger thousandth is 36.994 .
The next smaller thousandth is 36.992 .
Neither of those is any nearer to 36.993
than 36.993 already is.
The last '3' at the end of 36.993 is in the thousandths' place.
There is no more piece of another thousandth after it.
So 36.993 is already on a complete thousandth, and
there's no rounding required.
