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natta225 [31]
2 years ago
8

A bird leaves its nest and travels 20 miles per hour downwind for x hours. On the return trip, the bird travels 4 miles per hour

slower and has 6 miles left after x hours.
a. What is the distance of the entire trip?

miles

b. How long does the entire trip take?

hours
minutes and
seconds
Mathematics
1 answer:
Reil [10]2 years ago
7 0

Answer:

The correct answers are:

A) 60 miles; and B) 3.375 hours.

Explanation:

We will use the equation d = rt for this.

For the first leg of the trip, the bird travels 20 miles per hour for x hours.  This gives us the equation

d = 20x

For the return trip, the bird travels 4 miles per hour slower, so 20-4 = 16 miles per hour.  He also travels 6 miles less than the return distance, for x hours:

d-6 = 16x

To isolate d, we will add 6 to each side:

d-6+6 = 16x+6

d = 16x+6

We will set the two equations equal to one another, since they both equal d:

20x = 16x+6

Subtract 16x from each side:

20x-16x = 16x+6-16x

4x = 6

Divide both sides by 4:

4x/4 = 6/4

x = 1.5

He travels for 1.5 hours both times.

The first time, 1.5 hours at 20 miles per hour is:

d = 1.5(20) = 30 miles

The original trip is 30 miles.  This makes the entire trip 30(2) = 60 miles.

On the return trip, he travels 30-6 = 24 miles at 16 miles per hour:

24 = 16x

Divide both sides by 16:

24/16 = 16x/16

1.5 = x

If he goes 24 miles in 1.5 hours at 16 miles per hour, we can use a proportion to find the time it takes for the entire return trip:

24/1.5 = 30/x

Cross multiplying,

24*x = 1.5(30)

24x = 45

24x/24 = 45/24

x = 1.875

This gives him a total time of 1.5+1.875 = 3.375 hours

Step-by-step explanation:

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A vehicle uses 1 1/8 gallons of gasoline to travel 13 1/2 miles. At this rate, how many miles can the vehicle travel per gallon
valentina_108 [34]

Answer:

12 miles

Step-by-step explanation:

The problem above is related to the topic on "Equivalent Ratios." The missing term above is <em>"the number of miles that the vehicle can travel per gallon of gasoline."</em> In order to find this term, you have to use the "cross products."

Let n be the missing term.

  • 1\frac{1}{8} gallons/13\frac{1}{2} miles = \frac{1 gallon}{n}
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  • \frac{9}{8} x n = \frac{27}{2} x 1 gallon
  • n = \frac{27}{2} ÷ \frac{9}{8}
  • n = \frac{27}{2} x \frac{8}{9}
  • n = 12 miles

Therefore, the vehicle can travel 12 miles per gallon of gasoline.

3 0
3 years ago
it took Dean's family 3 hours to drive 195 miles on Friday. Then they drove at the same speed for 5 on saturday. how far did Dea
inn [45]

Hey!

Dean's family has been traveling on the same speed for two days, so to find how far you will need to travel you will need to find how far they are traveling in one hour..

To find this you will need to set up a proportion...

3/195 = 1/x

Solve this proportion by cross multiplying and then dividing..

195 * 1 = 195/3 = 65

This tells you that they are traveling 65 miles per hour. Now with this you will simply have to multiply 65 by 5 to tell you how far they would be traveling in 5 hours with the given speed...

65 * 5 = 325

Your answer of 325 miles tells you how far they traveled.


Hope it Helped!

~A

6 0
3 years ago
The area of a certain rectangle is 288 yd2. The perimeter is 68 yd. What are the dimensions of the rectangle?
arsen [322]

Answer:

The rectangle is 16*18

Step-by-step explanation:

The area of a rectangle is length * width and the perimeter is 2 times length * width

A = l*w

P = 2(l+w)

Replacing A and P

288 = l*w

68 = 2(l+w) => 34 = l+w => 34 - w = l

replacing l in the area

288 = (34 - w) w

w^2 - 34w + 288 = 0

(w - 16)(w - 18)

w = 16

w = 18

replacing in 34 - w = l

you get that when w = 16, l = 18 and when w = 18, l = 16

8 0
3 years ago
What is a rule that relates days to the amount earned? It's not Multiply by 9 because I put that and I got it wrong. So it's eit
ankoles [38]
It is multiply by 54 you are multiplying 54 by the hours you've worked to get the amount earned - which means you can find out the missing number for the sixth day. 36 times 54 equals 1,944.
4 0
3 years ago
If tan A = 4/3 and sin B = 45/53 and angles A and B are in Quadrant I, find the value of tan(A+B)
lbvjy [14]

Answer:

First, find tan A and tan B.

cosA=35 --> sin2A=1−925=1625 --> cosA=±45

cosA=45 because A is in Quadrant I

tanA=sinAcosA=(45)(53)=43.

sinB=513 --> cos2B=1−25169=144169 --> sinB=±1213.

sinB=1213 because B is in Quadrant I

tanB=sinBcosB=(513)(1312)=512

Apply the trig identity:

tan(A−B)=tanA−tanB1−tanA.tanB

tanA−tanB=43−512=1112

(1−tanA.tanB)=1−2036=1636=49

tan(A−B)=(1112)(94)=3316

kamina op bolte

✌ ✌ ✌ ✌

3 0
2 years ago
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