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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

1-4. Quiz

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Exercise 14 Page 242

Practice makes perfect

a Since we are given time, distance, and speeds, we can use the d=rt formula in order to right an equality.

d=rt The given distance is equal to 135 miles. The rate is equal to 55 mph on highways and 40 mph on the rest of the roads. If we let x represent the time we spend on the highways and y represent the time we spend on the rest of the roads, we can complete the equation. 55x+40y=135 Note that the time we spend on the highways and the time we spend on the rest of the roads sum up to 3 hours. x+y=3 If we combine the above equations we can form a system of equations. 55x+40y=135 & (I) x+y=3 & (II) In order to solve it we will use the Substitution Method.

55x+40y=135 & (I) x+y=3 & (II)

(II):LHS-x=RHS-x

55x+40y=135 & (I) y=3-x & (II)

(I):y= 3-x

55x+40( 3-x)=135 & (I) y=3-x & (II)

(I):Distribute 40

55x+120-40x=135 & (I) y=3-x & (II)

(I):Subtract term

15x+120=135 & (I) y=3-x & (II)

(I):LHS-120=RHS-120

15x=15 & (I) y=3-x & (II)

(I):.LHS /15.=.RHS /15.

x=1 & (I) y=3-x & (II)

(II):x= 1

x=1 & (I) y=3- 1 & (II)

(II):Subtract term

x=1 & (I) y=2 & (II)

In the context of the word problem, this means that we spend 1 hour driving at 55 mph and 2 hours at 40 mph.

b Since we want to calculate distances we will use the d=rt formula once again.

d=rtLet's substitute our speed on the highways as 55 mph and 1 hour we spend there.

d_h=r_ht_h

r_h= 55, t_h= 1

d_h=( 55)( 1)

a * 1=a

d_h=55

We can calculate the distance we drive on the rest of the roads the same way.

d_r=r_rt_r

r_r= 40, t_r= 2

d_r=( 40)( 2)

Multiply

d_r=80

This means that we drive 55 miles on the highways and 80 miles on the rest of the roads.

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Exercises p.242