10.03.2023

Dwayne drove 18 miles to the airport to pick up his father and then returned home. On the return trip he was able to drive an average of 15 miles per hour faster than he did on the trip there. If the total driving time was 1 hour, then what was his average speed driving to the airport? Someone please help

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Step-by-step answer

09.07.2023, solved by verified expert
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30 mph

Step-by-step explanation:

Let d = distance (in miles)

Let t = time (in hours)

Let v = average speed driving to the airport (in mph)

⇒ v + 15 = average speed driving from the airport (in mph)

Using:  distance = speed x time

Dwayne drove 18 miles to the airport to pick, №18009706, 10.03.2023 06:32

Create two equations for the journey to and from the airport, given that the distance one way is 18 miles:

Dwayne drove 18 miles to the airport to pick, №18009706, 10.03.2023 06:32

We are told that the total driving time is 1 hour, so the sum of these expressions equals 1 hour:

Dwayne drove 18 miles to the airport to pick, №18009706, 10.03.2023 06:32

Now all we have to do is solve the equation for v:

Dwayne drove 18 miles to the airport to pick, №18009706, 10.03.2023 06:32

Dwayne drove 18 miles to the airport to pick, №18009706, 10.03.2023 06:32

Dwayne drove 18 miles to the airport to pick, №18009706, 10.03.2023 06:32

Dwayne drove 18 miles to the airport to pick, №18009706, 10.03.2023 06:32

Dwayne drove 18 miles to the airport to pick, №18009706, 10.03.2023 06:32

Dwayne drove 18 miles to the airport to pick, №18009706, 10.03.2023 06:32

Dwayne drove 18 miles to the airport to pick, №18009706, 10.03.2023 06:32

As v is positive, v = 30 only

So the average speed driving to the airport was 30 mph

(and the average speed driving from the airport was 45 mph)

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Unlock the full answer

Let s represent the speed on the return trip

So, The initial speed will be (s-15)

Equation of time:

Dwayne drove 18 miles to the airport to pick, №18009706, 10.03.2023 06:32

return time + initial time = 1 hr

Dwayne drove 18 miles to the airport to pick, №18009706, 10.03.2023 06:32

⚘Solution for the complete equation in attachment!!~

Dwayne drove 18 miles to the airport to pick, №18009706, 10.03.2023 06:32

His average speed is 30 km/hr...~
Dwayne drove 18 miles to the airport to pick, №18009706, 10.03.2023 06:32
Dwayne drove 18 miles to the airport to pick, №18009706, 10.03.2023 06:32
It is was helpful?

Faq

Mathematics
Step-by-step answer
P Answered by Master

30 mph

Step-by-step explanation:

Let d = distance (in miles)

Let t = time (in hours)

Let v = average speed driving to the airport (in mph)

⇒ v + 15 = average speed driving from the airport (in mph)

Using:  distance = speed x time

\implies t=\dfrac{d}{v}

Create two equations for the journey to and from the airport, given that the distance one way is 18 miles:

\implies t=\dfrac{18}{v}  \ \ \textsf{and} \ \  t=\dfrac{18}{v+15}

We are told that the total driving time is 1 hour, so the sum of these expressions equals 1 hour:

\implies \dfrac{18}{v} +\dfrac{18}{v+15}=1

Now all we have to do is solve the equation for v:

\implies \dfrac{18(v+15)}{v(v+15)} +\dfrac{18v}{v(v+15)}=1

\implies \dfrac{18(v+15)+18v}{v(v+15)}=1

\implies 18(v+15)+18v=v(v+15)

\implies 18v+270+18v=v^2+15v

\implies v^2-21v-270=0

\implies (v-30)(v+9)=0

\implies v=30, v=-9

As v is positive, v = 30 only

So the average speed driving to the airport was 30 mph

(and the average speed driving from the airport was 45 mph)

Mathematics
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

Mathematics
Step-by-step answer
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
Mathematics
Step-by-step answer
P Answered by PhD

The answer is in the image 

The answer is in the image 
Mathematics
Step-by-step answer
P Answered by PhD

The solution is in the following image

The solution is in the following image
Mathematics
Step-by-step answer
P Answered by PhD

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

Mathematics
Step-by-step answer
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
Step-by-step answer
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

Mathematics
Step-by-step answer
P Answered by PhD

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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