Mathematics: Jacob rode his bicycle at an average rate of 15 kilometers per hour

Jacob rode his bicycle at an average rate of, №13393163, 02.03.2021 16:47

Mathematics

Joyce rode her bicycle 4 miles from her house to the library, and she rode the same distance from the library to the gym. her average speed from the library to the gym was 15 miles per hour less than her average speed from her house to the library. joyce modeled the trip from her house to the gym with the following expression. what does x - 15 represent in this situation? a. joyce s average speed from her house to the library b. the distance between the library and the gym c. joyce s average speed from the library to the gym d. the total time taken

Step-by-step answer

P Answered by Specialist

30

Alright, lets get started.

Please refer the diagram I have attached.

Joyce rode her bicycle 4 miles from her house to the library.

Suppose the average speed of Joyce = x miles per hours

She rode the same distance from the library to the gym means 4 miles.

Her average speed from the library to the gym was 15 miles per hour less than her average speed from her house to the library

So, the average speed from library to the gym will be = (x-15) miles per hour

So this expression is same as (x-15), the expression Joyce modeled.

Hence (x-15) repreents Joyce's average speed from the library to the gym.

So option C is correct answer. : Answer

Hope it will help :)

Mathematics

Joyce rode her bicycle 4 miles from her house to the library, and she rode the same distance from the library to the gym. her average speed from the library to the gym was 15 miles per hour less than her average speed from her house to the library. joyce modeled the trip from her house to the gym with the following expression. what does x - 15 represent in this situation? a. joyce s average speed from her house to the library b. the distance between the library and the gym c. joyce s average speed from the library to the gym d. the total time taken

Step-by-step answer

P Answered by Master

30

Alright, lets get started.

Please refer the diagram I have attached.

Joyce rode her bicycle 4 miles from her house to the library.

Suppose the average speed of Joyce = x miles per hours

She rode the same distance from the library to the gym means 4 miles.

Her average speed from the library to the gym was 15 miles per hour less than her average speed from her house to the library

So, the average speed from library to the gym will be = (x-15) miles per hour

So this expression is same as (x-15), the expression Joyce modeled.

Hence (x-15) repreents Joyce's average speed from the library to the gym.

So option C is correct answer. : Answer

Hope it will help :)

Mathematics

Jeremy rode his bicycle in a race. he averaged 15 mph and began the race 1 hour ahead of the other riders. the variable d represents jeremy s distance ridden, in miles. the variable t represents the number of hours since the other riders began to race. which equation can be used to determine the distance jeremy rode t hours into the race? d = 15t + 1 d=15(t+1) d=15(t−1) d=15t−1

Step-by-step answer

P Answered by PhD

3

d=15(t+1)

Step-by-step explanation:

The represents Jeremy's speed, which is 15 miles per hour.

The (t+1) represents the total number of hours Jeremy rode his bike, including the 1 hour head start he got. This adds his head start () and the rest of the time he has ridden ().

As mentioned in the problem, represents the total distance in miles that Jeremy rode on his bike.

Mathematics

Joyce rode her bicycle 4 miles from her house to the library, and she rode the same distance from the library to the gym. her average speed from the library to the gym was 15 miles per hour less than her average speed from her house to the library. joyce modeled the trip from her house to the gym with the following expression. what does x - 15 represent in this situation?

Step-by-step answer

P Answered by PhD

57

Call y the average speed from the library to the gym

Call x the average speed from the house to the library.

"Her average speed from the library to the gym was 15 miles per hour less than her average speed from her house to the library" => y = x - 15

So, x - 15 represents Joyces's average speed from her house to the libray to the gym.

Mathematics

Jeremy rode his bicycle in a race. he averaged 15 mph and began the race 1 hour ahead of the other riders. the variable d represents jeremy s distance ridden, in miles. the variable t represents the number of hours since the other riders began to race. which equation can be used to determine the distance jeremy rode t hours into the race? d = 15t + 1 d=15(t+1) d=15(t−1) d=15t−1

Step-by-step answer

P Answered by PhD

3

d=15(t+1)

Step-by-step explanation:

The represents Jeremy's speed, which is 15 miles per hour.

The (t+1) represents the total number of hours Jeremy rode his bike, including the 1 hour head start he got. This adds his head start () and the rest of the time he has ridden ().

As mentioned in the problem, represents the total distance in miles that Jeremy rode on his bike.

Mathematics

Carmen recently rode her bicycle to visit her friend who lives 12 miles away. On her way there, her average speed was 15 miles per hour faster than on her way home. If Carmen spent a total of 3 hours bicycling, find the two rates.

Step-by-step answer

P Answered by PhD

1

Carmen rode her bicycle at 20 miles per hour while riding to her friend house and while returning home she rode at speed of 5 miles per hour.

Step-by-step explanation:

Given:

Distance traveled = 12 miles

Total number of hours spent on bicycling = 3 hrs.

We need to find the speed while riding her friends house and rate while riding home.

Solution:

Let the speed while riding home be 'x'.

Now given:

On her way there, her average speed was 15 miles per hour faster than on her way home.

Speed while riding to her friends house = x+15

Now we know that;

Time is equal to distance divided by speed.

Time required to visit her friend house $t_1=\frac{12}{x+15}$

Time required while returning home $t_2=\frac{12}{x}$

Now we know that;

Total time she spent on bicycling is equal to sum of Time required to visit her friend house and Time required while returning home.

framing in equation form we get;

t_1+t_2 =3

Substituting the values of t_1 and t_2 we get;

$\frac{12}{x+15}+\frac{12}{x} = 3$

Now we will use LCM to make the denominator common we get;

$\frac{12x}{x(x+15)}+\frac{12(x+15)}{x(x+15)} = 3$

Now the denominator are common so we will solve the numerator.

$\frac{12x+12x+180}{x(x+15)}=3\\\\\frac{24x+180}{x(x+15)}=3$

By cross multiplication we get;

$24x+180=3x(x+15)\\\\24x+180=3x^2+45x\\\\3x^2+45x-24x-180=0\\\\3x^2+21x-180=0$

taking 3 common we get;

3(x^2+7x-60)=0

Dividing both side by 3 we get;

$\frac{3(x^2+7x-60)}{3}=\frac{0}{3}\\\\x^2+7x-60=0$

Now by factorizing the equation to find the roots we get;

$x^2+12x-5x-60=0\\\\x(x+12)-5(x+12)=0\\\\(x+12)(x-5)=0$

Now we will solve separately to find the value of x we get;

$x+12=0 \ \ \ \ Or \ \ \ \ x-5=0\\\\x=-12 \ \ \ \ \ \ \ Or \ \ \ \ \ x=5$

Now we have got 2 values of x one positive and one negative.

we know that time cannot be negative and hence we will discard the negative value of x and consider the positive value of x.

speed while riding home = $5\ mi/hr$

Speed of bicycle while visiting her friend house = $x+15 = 5+15 =20\ mi/hr$

Hence Carmen rode her bicycle at 20 miles per hour while riding to her friend house and while returning home she rode at speed of 5 miles per hour.

Mathematics

Carmen recently rode her bicycle to visit her friend who lives 12 miles away. On her way there, her average speed was 15 miles per hour faster than on her way home. If Carmen spent a total of 3 hours bicycling, find the two rates.

Step-by-step answer

P Answered by PhD

1

Carmen rode her bicycle at 20 miles per hour while riding to her friend house and while returning home she rode at speed of 5 miles per hour.

Step-by-step explanation:

Given:

Distance traveled = 12 miles

Total number of hours spent on bicycling = 3 hrs.

We need to find the speed while riding her friends house and rate while riding home.

Solution:

Let the speed while riding home be 'x'.

Now given:

On her way there, her average speed was 15 miles per hour faster than on her way home.

Speed while riding to her friends house = x+15

Now we know that;

Time is equal to distance divided by speed.

Time required to visit her friend house $t_1=\frac{12}{x+15}$

Time required while returning home $t_2=\frac{12}{x}$

Now we know that;

Total time she spent on bicycling is equal to sum of Time required to visit her friend house and Time required while returning home.

framing in equation form we get;

t_1+t_2 =3

Substituting the values of t_1 and t_2 we get;

$\frac{12}{x+15}+\frac{12}{x} = 3$

Now we will use LCM to make the denominator common we get;

$\frac{12x}{x(x+15)}+\frac{12(x+15)}{x(x+15)} = 3$

Now the denominator are common so we will solve the numerator.

$\frac{12x+12x+180}{x(x+15)}=3\\\\\frac{24x+180}{x(x+15)}=3$

By cross multiplication we get;

$24x+180=3x(x+15)\\\\24x+180=3x^2+45x\\\\3x^2+45x-24x-180=0\\\\3x^2+21x-180=0$

taking 3 common we get;

3(x^2+7x-60)=0

Dividing both side by 3 we get;

$\frac{3(x^2+7x-60)}{3}=\frac{0}{3}\\\\x^2+7x-60=0$

Now by factorizing the equation to find the roots we get;

$x^2+12x-5x-60=0\\\\x(x+12)-5(x+12)=0\\\\(x+12)(x-5)=0$

Now we will solve separately to find the value of x we get;

$x+12=0 \ \ \ \ Or \ \ \ \ x-5=0\\\\x=-12 \ \ \ \ \ \ \ Or \ \ \ \ \ x=5$

Now we have got 2 values of x one positive and one negative.

we know that time cannot be negative and hence we will discard the negative value of x and consider the positive value of x.

speed while riding home = $5\ mi/hr$

Speed of bicycle while visiting her friend house = $x+15 = 5+15 =20\ mi/hr$

Hence Carmen rode her bicycle at 20 miles per hour while riding to her friend house and while returning home she rode at speed of 5 miles per hour.

Mathematics

On his bicycle, trevor rode 15 miles in 30 minutes. what was his average rate of speed?

Step-by-step answer

P Answered by PhD

1

0.5 miles/min

Step-by-step explanation:

average speed = total distance / total time

= 15 miles / 30 min

= 0.5 miles/min

Mathematics

On his bicycle, trevor rode 15 miles in 30 minutes. what was his average rate of speed?

Step-by-step answer

P Answered by PhD

1

0.5 miles/min

Step-by-step explanation:

average speed = total distance / total time

= 15 miles / 30 min

= 0.5 miles/min

Mathematics

Neil places £2000 in a bank account that pays 1.5% simple interest per year. How much interest will he earn in 6 years?

Step-by-step answer

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

Jacob rode his bicycle at an average rate of 15 kilometers per hour

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