A and B together can do a work in 6 days. If A alone can do it in 15 days. In how many days can B alone do it.
2 answers:
Answer:
10 days to complete
Step-by-step explanation:
for mixed rate problems, the sum of each individual reciprocal rates equals the sum of the combined rate
i.e
we are given,
A's rate = 15 days to complete
Combined rate = 6 days to complete
B's rate = need to find
substituting' the given info into the equation above,
1/15 + 1/ (B's Rate) = 1/6
1 / (B's Rate) = 1/6 - 1/15 (convert right side to same denominator)
1 / (B's Rate) = 5/30 - 2/30
1 / (B's Rate) = 3/30
1 / (B's Rate) = 1/10 (taking reciprocal of both sides)
B's rate = 10 days to complete
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The absolute value function |<em>x</em>| always returns a non-negative number. It takes any number <em>x</em> and returns <em>x</em> if it's already non-negative, or -<em>x</em> if it is negative in order to make it positive.
For the equation
-3 + 4 |2<em>x</em> - 5| = 14
rearrange terms to get
|2<em>x</em> - 5| = 17/4
Now,
• if 2<em>x</em> - 5 ≥ 0, then |2<em>x</em> - 5| = 2<em>x</em> - 5. Then
2<em>x</em> - 5 = 17/4
• and if instead 2<em>x</em> - 5 < 0, then |2<em>x</em> - 5| = -(2<em>x</em> - 5), so that
-(2<em>x</em> - 5) = 17/4, or
2<em>x</em> - 5 = -17/4
In the first case,
2<em>x</em> - 5 = 17/4
2<em>x</em> = 17/4 + 5 = 37/4
<em>x</em> = 37/8
In the second case,
2<em>x</em> - 5 = -17/4
2<em>x</em> = -17/4 + 5 = 3/4
<em>x</em> = 3/8