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

. 0

Step-by-step answer

09.07.2023, solved by verified expert
Unlock the full answer

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)

It is was helpful?
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
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 answer is in the image 

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

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

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.

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.

Mathematics
Step-by-step answer
P Answered by PhD

Cost before sale tax=$46.00

Cost after including tax=$48.76

Sale tax=$48.76-46.00

=$2.76

we know,

sale tax=((sales tax rate)/100) * cost before sale tax

2.76=((sales tax rate)/100) *46.00

sale tax rate=(2.76*100)/46

                   =276/46

                    =6%

There fore sales tax rate=6%

Mathematics
Step-by-step answer
P Answered by PhD

The solution is given below

The solution is given below

Try asking the Studen AI a question.

It will provide an instant answer!

FREE