1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
iris [78.8K]
3 years ago
15

George and Paula are running around a circular track. George starts at the westernmost point of the track, and Paula starts at t

he easternmost point. The illustration below shows their starting positions and running directions. They start running toward each other at constant speeds. George runs at 9 feet per second. Paula takes 50 seconds to run a lap of the track. George and Paula pass each other after 14 seconds.
After running for 4 minutes, how far east of his starting point is George?

Mathematics
1 answer:
arsen [322]3 years ago
6 0

Answer:

George is 43.20 ft East of his starting point.

Step-by-step explanation:

Let Paula's speed be x ft/s

George's speed = 9 ft/s

Note that speed = (distance)/(time)

Distance = (speed) × (time)

George takes 50 s to run a lap of the track at a speed of y ft/s

Meaning that the length of the circular track = y × 50 = 50y ft

George and Paula meet 14 seconds after the start of the run.

Distance covered by George in 14 seconds = 9 × 14 = 126 ft

Distance covered by Paula in 14 seconds = y × 14 = 14y ft

But the sum of the distance covered by both runners in the 14 s before they first meet each other is equal to the length of the circular track

That is,

126 + 14y = 50y

50y - 14y = 126

36y = 126

y = (126/36) = 3.5 ft/s.

Hence, Paula's speed = 3.5 ft/s

Length of the circular track = 50y = 50 × 3.5 = 175 ft

So, in 4 minutes (240 s), with George running at 9 ft/s, he would have ran a total distance of

9 × 240 = 2160 ft.

2160 ft around a circular track of length 175 ft, means that George would have ran a total number of laps (2160/175) = 12.343 laps.

Breaking this into 12 laps and 0.343 of a lap from the starting point. 0.343 of a lap = 0.343 × 175 = 60 ft

So, 60 ft along a circular track subtends an angle θ at the centre of the circle.

Length of an arc = (θ/360°) × 2πr

2πr = total length of the circular track = 175

r = (175/2π) = 27.85 ft

Length of an arc = (θ/360) × 2πr

60 = (θ/360°) × 175

(θ/360°) = (60/175) = 0.343

θ = 0.343 × 360° = 123.45°

The image of this incomplete lap is shown in the attached image,

The distance of George from his starting point along the centre of the circular track = (r + a)

But, a can be obtained using trigonometric relations.

Cos 56.55° = (a/r) = (a/27.85)

a = 27.85 cos 56.55° = 15.35 ft

r + a = 27.85 + 15.35 = 43.20 ft.

Hence, George is 43.20 ft East of his starting point.

Hope this Helps!!!

You might be interested in
If I have 10 crates of beer each with 12 bottles inside, selling each for R19.00 (South African currency Rand), how much money w
lakkis [162]

Answer: R2280

Step-by-step explanation:

Total crates = 10

Bottles in one crate = 12

Total bottles = 10 x 12 = 120

Price of 1 bottle = R19

Price of 120 bottles = R19 x 120 = R2280

8 0
2 years ago
Read 2 more answers
Write a complete sentence that states the type of transformation that was performed and explains the transformation in detail. Q
Cerrena [4.2K]
The type of transformation that has happened is a translation. Translation is when the image's size nor shape changes after transformation. every point in the image moves the same distance in the same direction.
the equation for the translation mentioned is;
T4, -5(x,y)
this means that every point in the image has moved down by 5 units and moved to the right by 4 units.
Point A to Point E
Point A - (-4,-1)
after translation (x+4, y-5) = (-4+4,-1-5)
                                          = (0,-6) these are the coordinates of point E.
the other three points too have moved the same distance and direction as point  A did.

4 0
3 years ago
Lit. Bhfgggggggggggghggggggg
Archy [21]

Answer:

Image isn't popping up

Step-by-step explanation:

8 0
3 years ago
How many square centimetres are in 0.0075 square metres
lidiya [134]

Answer:

75 square centimeters

Step-by-step explanation:

Multiply by 10,000

Can you make me brainliest it would help a lot!

4 0
3 years ago
Read 2 more answers
A drainage basin bordering the sea has an area of 7500 km2 . The average precipitation for this drainage basin is 900 mm year-1
Alexxx [7]

Answer with Step-by-step explanation:

The basic water balance dictates that "Amount of water flowing into the basin should be equal to the amount of water flowing out of it".

Mathematically

Water_{in}=Water_{out}\\\\P=E+Q+I

where

P = precipitation

I = Infiltration losses in the basin

E = Evapotranspiration

Q = is outflow from the basin

Applying the given values we get

900=E+\frac{22.5\times 10^{8}}{7500\times 10^{6}}\times 1000+100\\\\900=E+300+100

Part b)

From the above equation we get

E=900-400=500mm/year

The evaporation in cubic meters per year is

E'=0.5\times 7500\times 10^{6}=3750\times 10^{6}m^3/year

7 0
3 years ago
Other questions:
  • Wildlife resort has eight elephant cabs born during the summer and now has 31 total how many elephants were ending was there bef
    15·1 answer
  • To make one cheese sandwich, Tina uses one bread roll and two cheese slices.
    15·1 answer
  • Solve the equation using the quadratic formula -x^2+27=6x
    10·2 answers
  • Checking account a has a service fee of $3 and a per check fee of $0.02 while checking account b charges a monthly fee of $2
    12·2 answers
  • Troy and Jared are eating carrots if they each can eat two carrots in 3 minutes how long will it take the two of them to eat 18
    14·2 answers
  • -Mondays 10 points<br> -Wednesdays 10 points<br> -Fridays 30points<br> -Sundays 10 points
    8·2 answers
  • Using the function below, evaluate f(-2). *<br> 2 points<br> f(x) = 3x? - 5x - 2
    8·1 answer
  • PLEASE HELP ME WITH THIS ASAP!! only one question
    12·1 answer
  • On monday andres bought a new bike for 112.50 if his bike depreciates by 15% what is his bike worth now
    12·1 answer
  • Complete the table for the equation
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!