Question 655559
1) It takes Molly 5 minutes longer to dig a hole that it takes Holly. If they dig the hole together, it takes them 6 minuites. How long would it take Molly to dig a hole by herself? (round to nearest tenth)
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Molly takes m minutes to dig the hole alone.
Holly takes h minutes...
"It takes Molly 5 minutes longer to dig a hole that it takes Holly" --> m = h+5

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Molly digs the hole in m minutes, so each minute she digs 1/m of the hole
Holly digs 1/h of the hole.
Together, they dig 1/m + 1/h of the hole, and it takes them 6 minutes.
--> 1/m + 1/h = 1/6
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Now it's not a "word problem."
1/m + 1/h = 1/6
m = h+5
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1/m + 1/h = 1/6
Multiply thru by 6mh to eliminate the fractions.
6h + 6m = h*m
Sub for m in the 1st equation
6h + 6(h+5) = h*(h+5)
6h + 6h+30 = h^2 + 5h
{{{h^2 - 7h - 30 = 0}}}
(h - 10)*(h + 3) = 0
h = -3 Ignore, they can't do it in -3 minutes.
h = 10 minutes
Holly's time alone
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m = h+5 = 15 minutes
Molly's time alone.
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That's a complex problem, don't feel bad about needing help.
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2) Willie paddled 12 miles up the creek and then paddled 12 miles back. If the speed of the current was 3mph and the total trip took 4 hours, what was Willie's speed?
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w = Willie's paddling speed
c = speed of current = 3 mi/hr
Upstream, he moved at (w-c) mi/hr
Downstream, it's (w+c) mi/hr
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d = r*t
t = d/r
t = 12/(w-3) + 12/(w+3) = 4
12/(w-3) + 12/(w+3) = 4
Can you finish that?