Ask question

Ask question

All categories

3 years ago

6

Emma started biking to the coffee shop traveling 15 mph, after some time the bike got a flat so Emma walked the rest of the way,

traveling 7 mph. If the total trip to the coffee shop took 9 hours and it was 103 miles away, how long did Emma travel at each speed

1 answer:

serious [3.7K]3 years ago

4 0

Answer:

$75\text{ miles, }28\text{ miles}$

Step-by-step explanation:

GIVEN: Emma started biking to the coffee shop traveling $15 \text{mph}$ , after some time the bike got a flat so Emma walked the rest of the way, traveling $7 \text{mph}$ If the total trip to the coffee shop took $9 \text{hours}$ and it was $103 \text{miles}$ away.

TO FIND: how long did Emma travel at each speed.

SOLUTION:

Let the distance traveled by Emma through bike is $\text{x}$

Total time taken when traveled by bike $=\frac{\text{x}}{15}$

Distance traveled through feet $=103-\text{x}$

Total time taken when traveled by feet $=\frac{103-\text{x}}{7}$

Now,

Total time taken $=9\text{hours}$

$\frac{\text{x}}{15}+\frac{103-\text{x}}{7}=9$

$8\text{x}=600$

$\text{x}=75$

Distance traveled through feet $=103-75=28\text{miles}$

Hence distance traveled using bike is $75\text{miles}$ and by feet is $28\text{miles}$

You might be interested in

Write an equation of the line that passes through the given point and has the given slope.

Minchanka [31]

Answer:

y = -x - 4

Step-by-step explanation:

the equation of a linear graph is y = mx + b

you know the m = -1

so now the equation is y = -x + b

from here, what you could do to find b is...

plug (-1, -3) into the equation

1) x = -1, y = -3

2) -3 = -(-1) + b

3) -3 = 1 + b

4) -4 = b

or you can look at the y-intercept which is where the line intersects with the y-axis

it seems to be (0, -4)

so "b" would be equal to -4

this makes the final equation y = -x + (-4) or y = -x - 4

4 0

2 years ago

If a barber is capable of cutting the hair of 35 people per day and he works 7 days per week, how many haircuts could he give du

Pavel [41]

June=1,225
April=1,225
May=1,225

All June April and May is 3,675 haircuts

6 0

3 years ago

Can someone answer pleaseee!

Scilla [17]

Answer:

The answer would be D

Step-by-step explanation:

It is a Pentagon it has 5 sides and the discription said I had 4 sides

4 0

3 years ago

HELP: I need help on multiple questions for a quiz before tomorrow night. If all is answered, you will get 40+ points and marked

Vinil7 [7]

Answer:

1. $33,000

2. $6077.53

3.

a) 2.72 seconds

b) 0.96 seconds

4. 189 square meters

5.

a) Average Rate of Change = 4 pounds per week, or -4

b) 160 pounds (after 5 weeks)

6.

Independent Variables = p, A, and H

Dependent Variable = T

141 beats per minute (rounded to nearest whole number)

Step-by-step explanation:

1.

The value of a tractor V(t) decreases over time, t. Its value is given by:

$V(t)=55000-5500t$

To find value of tractor after 4 years, we would need to substitute "4" into t and calculate. It is shown below:

$V(t)=55000-5500t\\V(4)=55000-5500(4)\\V(4) =33000$

The value of the tractor after 4 years is <u>$33,000</u>

<u></u>

2.

The value of investment that is growing each year, is given by:

$f(n)=5000(1.05)^{n}$

Where

5000 is the initial investment (deposit)

1.05 means a 5% growth rate per year

n is the time in years

We want the investment's value after 4 years, so n would be 4. Substituting we get our answer:

$f(n)=5000(1.05)^{n}\\f(4)=5000(1.05)^{4}\\f(4)=6077.53$

To the nearest cent, the value of the investment would be:

<u>$6077.53</u>

<u></u>

3,

The time it takes of pendulum to make one swing is given by the formula:

$T(L)=2\pi \sqrt{\frac{L}{32}}$

Where L is the length of the pendulum in feet

a)

If L = 6ft, the time it will take is:

$T(6)=2\pi \sqrt{\frac{6}{32}}\\T(6)=2.72$

About <u>2.72 seconds</u>

<u></u>

b)

Now, the length is 9 inches, we convert it to feet first:

9/12 = 0.75 feet

So, the time it will take:

$T(0.75)=2\pi \sqrt{\frac{0.75}{32}}\\T(0.75)=0.96$

So, it will take about <u>0.96 seconds</u>

<u></u>

4.

The area of weed after t days can be modeled by:

$A(t)=0.006 \pi t^2$

Where t is number of days

Now, we want to find area after 100 days, so let t = 100, we get:

$A(t)=0.006 \pi t^2\\A(100)=0.006 \pi (100)^2\\A(100)=188.5$

Rounded to nearest sq. m, we have the area to be:

<u>189 square meters</u>

<u></u>

5.

a)

The avg. rate of change is basically how much the program is advertising that someone can loose in a week. It says "4 pounds per week". Since decrease, we give the value of "4" and negative sign So:

<u>Average Rate of Change = 4 pounds per week, or -4</u>

<u></u>

b)

Initial weight is 180 pounds, we know 4 pounds is decreased every week when going through the program course. So, after 5 weeks,

5 * 4 = 20 pounds will be less

So, he will be:

180 - 20 = <u>160 pounds (after 5 weeks)</u>

6.

The Karvonen formula is given as:

$T=p(220-A)+H(1-p)$

Where

T is target heart rate (in bpm)

p is the percent intensity (expressed as decimal)

A is the age (in yrs)

H is the resting heart rate (in bpm)

We need to identity the independent and dependent variables. Now, lets that a simple example:

y = 2x

Here,

x is the independent variable

y is dependent on x, so y in dependent

Similarly, if you look at the formula, you can see:

p, A, and H are all independent

T depends on them

So,

p, A, H are independent variables

T is the dependent variable

<u>Independent Variables = p, A, and H</u>

<u>Dependent Variable = T</u>

<u></u>

We are given

A = 35

H = 60

p = 65% = 65/100 = 0.65

Now, we want T, lets substitute and find:

$T=0.65(220-35)+60(1-0.65)\\T=141.25$

<u>The target heart rate should be: 141 beats per minute (rounded to nearest whole number)</u>

<em><u /></em>

<em><u /></em>

3 0

3 years ago

4<br> It takes Joaquin hour to hike mile. What is Joaquin’s unit rate, in miles per hour?

torisob [31]

He is walking 1 mile/hour. If it takes him one hour to hike a mile then he is going one mile and hour.

Hope that helps.

4 0

3 years ago

Read 2 more answers