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notsponge [240]
3 years ago
11

The first row I️n the auditorium has 42 seats.each row after the first has 3 more seats than the row before I️t

Mathematics
2 answers:
Papessa [141]3 years ago
6 0

s = 3r + 42
s is the number of seats
r is the row number

3 because they increase by that each row
+42 because the starting row has 42

A
s = 3r + 42 \\ s = 3(25) + 42 \\ s = 75 + 42 \\ s = 117
B

s = 3r + 42 \\ 90 = 3r + 42 \\ 90 - 42 = 3r \\ 48 \div 3 = 3r \div 3 \\ 16 = r

grandymaker [24]3 years ago
4 0
A. 117 seats
B. row 16
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Roberto rowed 20 miles downstream in 2.5 hours. The trip back, however, took him 5 hours. Find the rate that Roberto rows in sti
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Answer:

<em>Roberto's speed in still water is 6 miles/hour and the river speed is 2 miles/hour</em>

Step-by-step explanation:

<u>Relative Speed</u>

When a body is moving at a constant speed v, the distance traveled in a time t is:

d=v.t

When Roberto rows downstream, his speed in still water is added to the speed of the water, making it easier to travel the required distance.

When Roberto rows upstream, his speed in still water is affected by the speed of the water, both are subtracted and the required distance is covered in more time.

Let's call

x = Roberto's rowing speed in still water

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20=(x+y)*2.5

Rearranging, we find the downstream equation:

2.5x+2.5y=20\qquad[1]

The speed when rowing upstream is x-y, and the distance traveled is

d=(x-y).t_2

Where t2=5 hours. Substituting values:

20=(x-y)*5

Rearranging, we find the upstream equation:

5x-5y=20\qquad[2]

Multiplying [1] by 2:

5x+5y=40

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10x=60

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x=60/10=6

Dividing [2] by 5:

x-y=4

Solving for y

y=x-4=6-4=2

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