28.05.2023

# Jen recently rode her bicycle to visit her friend who lives 12 miles away. On her way there, her average speed was 7 miles per hour faster than on her way home. If Jen spent a total of 1 hour bicycling, find the two rates.

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02.10.2022, solved by verified expert
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Rate while going to her friend's home = 28 mph
Rate while her way back home = 21 mph

Step-by-step explanation:

Let the average speed of Jen while her way back home be x mph.

So, her average speed while going to her friend's home = (x + 7)mph

Now, distance = 12 km

So, time taken while going to her friend's home = Distance/speed = 12/(x + 7) hours

Time taken while coming her way back home = Distance/speed = 12/x hours

Now, total time taken = 1 hour

Thus,

12/x + 12/(x + 7) = 1

(12x + 84 + 12x)/x(x + 7) = 1

24x + 84 = x(x + 7)

24x + 84 = x² + 7x

x² - 17x - 84 = 0

Putting -17x = 4x - 21x,

x² + 4x - 21x - 84 = 0

x(x + 4) - 21(x + 4) = 0

(x + 4)(x - 21) = 0

So, x = -4 or x = 21

Since speed cannot be negative, so x = 21 mph

Thus,

Rate while going to her friend's home = x + 7 = 21 + 7 = 28 mph

Rate while her way back home = x = 21 mph

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### Faq

Mathematics
P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Mathematics
P Answered by PhD
Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram
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For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

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y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=\$53

Therefore, Value after 19 years=\$53

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The answer is in the image

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P Answered by PhD

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

=4300/3.3

=1303.03kg

Mathematics
P Answered by PhD

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

=4300/3.3

=1303.03kg

Approximately it is aqual to 1300kg

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P Answered by PhD

Here,

tip=18%of \$32

tip=(18/100)*32

=0.18*32

=\$5.76

Total payment=32+5.76=\$37.76

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The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

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