Monica reads 7 1/2 pages of a mystery book in 9 minutes what’s her average reading rate in pages per minute

Two cyclists, Alan and Brian, are racing around oval track of length 450m on the same direction simultaneously from the same poi

skelet666 [1.2K]

Answer:

Alan: 200 m/min

Brian: 150 m/min

Step-by-step explanation:

Given : Two cyclists, Alan and Brian, are racing around oval track of length 450m on the same direction simultaneously from the same point. Alan races around the track in 45 seconds before Brian does and overtakes him every 9 minutes.

To find : What are their rates, in meters per minute?

Solution :

Let n represent the number of laps that Alan completes in 9 minutes.

Then n-1 is the number of laps Brian completes.

45 seconds = 3/4 minutes.

The difference in their lap times in minutes per lap is

$\frac{9}{(n -1)}-\frac{9}{n} =\frac{3}{4}$

Solving the equation we get,

$\frac{9n-9n+9}{n(n -1)} =\frac{3}{4}$

$9\times 4=3\times n(n -1)$

$36=3\times n(n -1)$

$n^2-n-12=0$

$n^2-4n+3n-12=0$

$n(n-4)+3(n-4)=0$

$(n-4)(n+3)=0$

$n=4,-3$

Neglecting n=-3

So, n=4

Then Alan's speed in m/min is

$S=\frac{D}{T}$

$S_a=\frac{4\times 450}{9}$

$S_a=200 m/min$

Brian completes 3 laps in that 9-minute time, so his rate is

$S_b=\frac{3\times 450}{9}$

$S_b=150 m/min$

Therefore, Alan: 200 m/min

Brian: 150 m/min

4 0

4 years ago

Factorise<br>ab+cb+ad+cd

sweet-ann [11.9K]

Answer:

Factorized abaabababba

Step-by-step explanation:

yeet

3 0

3 years ago

Given that f(x) = 4x - 3 and g(x) 2x-1 divided by 3<br><br> solve for g(f(2))

scZoUnD [109]

Answer:

2nd option = 3 is the answer.

4 0

3 years ago

Carlos and Maria drove a total of 233 miles in 4.4 hours. Carlos drove the first part of the trip and averaged 55 miles per hour

11Alexandr11 [23.1K]

So basically
D=RT
distance=rate times time

D=233
carlos speed=55
maria speed=50
total time=4.4 hours

so therefor we have to represent
carlos time
maria time
carlos distance
maria dstance

let's say that
remember that whatever carlost drove is 233 minus maria (time and distance)
and since we are solving for maria time and distnace, solve in terms of them
maria time=t
maria distance=d
carlos time=4.4-t
carlos distance=233-d

remember total D=RT
find their seperate equations
carlos
233-d=55(4.4-t)

maria
d=50(t)
use them to solve

233-d=55(4.4-t)
subsitute 50(t) for d
233-50t=55(4.4-t)
add 50t to both sides
233=55(4.4-t)+50t
distribute using distributiver protperty (a(b+c)=ab+ac)
55(4.4-t)=242-55t
233=242-55t+50t
add like terms
233=242-5t
add 5t to both sides
233+5t=242
subtract 233 from both sides
5t=9
divdie both sides by 5
t=1.8
maria drove 1.8 hours

the answer is A

8 0

3 years ago

A ribbon is 30cm long and it is cut into three pieces such that each piece is 2cm longer than the next. Represent this as an equ

Alisiya [41]

Answer:

Step-by-step explanation:

3 pieces such that each piece is 2 cm longer then the next...

x , x + 2, x + 4

x + x + 2 + x + 4 = 30

3x + 6 = 30

3x = 30 - 6

3x = 24

x = 24/3

x = 8

x + 2 = 8 + 2 = 10

x + 4 = 8 + 4 = 12

check...

8 + 10 + 12 = 30

18 + 12 = 30

30 = 30 (correct)...it checks out

the ribbon lengths are : 8 cm, 10 cm, and 12 cm

3 0

4 years ago

Read 2 more answers