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Material Type: Quiz; Class: Intermediate Algebra; Subject: Mathematics; University: Utica College; Term: Spring 2005;
Typology: Quizzes
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Friday, January 28, 2005
2(x − y) − 4(x + y)
2(x − y) − 4(x + y) = 2 x − 2 y − 4 x − 4 y distribute the 2 and the - = − 2 x − 6 y combine like terms
−3(1 − 4 x) − 2(2x − 1) = 12x
−3(1 − 4 x) − 2(2x − 1) = 12x =⇒ −3 + 12x − 4 x + 2 = 12x =⇒ −1 + 8x = 12x combine like terms =⇒ −1 = 4x subtract 8x from both sides =⇒ x = −
divide by 4
y + 2x = 4x − 3 y − 6 =⇒ y − 2 x = − 3 y − 6 subtract 4x =⇒ − 2 x = − 4 y − 6 subtract y =⇒ x = 2y + 3 divide by − 2
(a) How long does it take for Skippy to drive to Syracuse? Skippy drives at a rate of 60 miles per hour over a distance of 50 miles. So plugging these values into D = rt, we have
D = rt =⇒ 50 = 60 t =⇒ t =
hours
=⇒ t =
hours ·
60 minutes hour =⇒ t = 50 minutes
(b) How much time does Noodle have to drive to Syracuse? Skippy has a 15 minute head start on Noodle, who is going to take 50 minutes to get there. So in order to reach Syracuse at the same time as Skippy, Noodle will have to get there in
50 − 15 = 35 minutes.
(c) How fast does Noodle have to drive in order to arrive in Syracuse at the same time as Skippy? We have to watch our units on this one. Noodle needs to get there in 35 minutes, which we convert to
35 60
hours
He needs to cover a distance of 50 miles in 7/12 of an hour. So, using our trusty D = rt formula for Uniform Motion Problems, we get
D = rt =⇒ 50 = r
=⇒ r =
=⇒ r =
mph =⇒ r ≈ 85 .7 mph
