Short Answer: 18 minutes
Remark
The answer to this problem is less than the smallest time of the two people working together. that fact lets out C and D (38 minutes and 75 minutes). Now you have to choose 15 minutes and 18 minutes. There's a method. No guessing needed.
Givens
Let the time for Sophie = S
Let the time for Simon = M
Let the job to completion = 1
S = 45 minutes
M = 30 minutes
Step One
Convert minutes to hours.
45 minutes = 45 / 60 = 3/4 hour = 0.75 hour
30 minutes = 30 / 60 = 1/2 hour = 0.50 hour
Step Two
Set up the Equation
The formula is a form of job / hour.
Let the time = t that they both have to work
job = 1 in these problems.
1/S + 1/M = 1/t
1/0.75 + 1/0.5 = 1/t
Solve
1 ÷ 0.75 = 1.33333
1 ÷ 0.5 = 2
1.3333 + 2 = 3.33333
3.3333 = 1 / t Multlply both sides by t
3.3333*t = 1
t = 1 / 3.333333333
t = 0.3 of an hour
1 hour = 60 minutes
0.3 hours = x Cross Multiply
x = 60 * 0.3
x = 18 minutes
Answer working together it took them 18 minutes <<<<<
<span>Find
the values of a and b that make f continuous everywhere. f(x) = x^2 − 4
/ x − 2 if x < 2 ax^2 − bx + 3 if 2 ≤ x < 3 4x − a + b if x ≥ 3
</span>
a=7/12
b=13/2
Add like terms and put x in the middle.
-3 < -2x + x - 3x ≤ 5 - 2
-3 < - 4x ≤ 3
Sign changed when divide by negative numbers
(3/4) > x ≥ (-3/4)
