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Lady bird [3.3K]
3 years ago
15

6x - 12 = 2 (3x - 9) + 6

Mathematics
1 answer:
sergey [27]3 years ago
6 0

Answer:

6x + -12 = 3x + 9

Reorder the terms:

-12 + 6x = 3x + 9

Reorder the terms:

-12 + 6x = 9 + 3x

Solving

-12 + 6x = 9 + 3x

Step-by-step explanation:

12 + 6x = 9 + 3x

-12 + 6x = 9 + 3x

-12 + 6x + -3x = 9 + 3x + -3x

6x + -3x = 3x

-12 + 3x = 9 + 3x + -3x

3x + -3x = 0

-12 + 3x = 9 + 0

-12 + 3x = 9

-12 + 12 + 3x = 9 + 12

-12 + 12 = 0

0 + 3x = 9 + 12

3x = 9 + 12

9 + 12 = 21

3x = 21

Divide each side by 3

x = 7

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Mr. Jones lives in City A and drives at a constant speed to City B, which is 400 km 2 of the distance at that same away. On the
Sphinxa [80]

Answer:

He traveled at 72km/hr during the rain

Step-by-step explanation:

<em>Question is not well formatted. See comment</em>

Given

d=400km --- distance

t = 11hrs --- total time

Let his speed from city A till the rain starts on his return trip be s_1

Let his speed from city during the rain be s_2

So:

s_2 = s_1 -20

Required

Calculate s_2

From the question, we understand that; he drives the whole 400 km and 2/5 of 400 km at s_1

The distance covered during this period is:

d_1  = 400 + \frac{2}{5} * 400

d_1  = 400 + 160

d_1  = 560

And the time during this period is:

t_1 = \frac{2}{5} * 11

t_1 = 4.4

So, the distance during the rain is:

d_2 = 2 * 400 - d_1

d_2 = 2 * 400 - 560

d_2 = 800 - 560

d_2 = 240

And the time during the rain is:

t_2 = 11 - t_1

t_2 = 11 - 4.4

t_2 = 6.6

So, we have:

d_1  = 560 --- distance covered before the rain

d_2 = 240 --- distance covered when raining

s_2 = s_1 -20

t_1 = 4.4 ---- time spent before the rain

t_2 = 6.6 --- time spent in the rain

Speed is calculated as:

Speed = \frac{distance}{time}

Make distance the subject

distance = speed * time

So:

d_1 + d_2 = s_1 * t_1 + s_2 * t_2

Recall that:

s_2 = s_1 -20

Make s_1 the subject

s_1 = s_2 + 20

The expression d_1 + d_2 = s_1 * t_1 + s_2 * t_2 becomes:

560 + 240 = (s_2 + 20) * 4.4 + s_2 * 6.6

800 = 4.4s_2 + 88+ 6.6s_2

Collect like terms

6.6s_2 + 4.4s_2 = 880 - 88

11s_2 = 792

Solve for s_2

s_2= \frac{792}{11}

s_2=72km/h

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Answer:

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