George and Paula are running around a circular track. George starts at the weste

Question

George and Paula are running around a circular track. George starts at the westernmost point of the track, and Paula starts at the easternmost point. The illustration below shows their starting positions and running directions. They start running toward each other at constant speeds. George runs at 8 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? (Round your answer to three decimal places.)

Explanation / Answer

George : 8 ft/sec
Paula takes 50 secs
They meet after 14 secs...

Let speed of Paula be x.

We have circumference = C

when they pass, they will have travelled a total distance of C/2

(C/2) / (8 + x) = 14
C = 28(8 + x)

C/x = 50
28(8 + x)/x = 50

Crossmultiply :
28(8 + x) = 50x

14(8 + x) = 25x

112 + 14x = 25x

11x = 112

x = 112/11 ft/sec

C/x = 50
C = 50x

C = 50*112/11

C = 5600/11 feet is the length of the lap

Now, 4 min = 4*60 = 240 seconds...

In 240 sec, George covers 240*8 = 1920 feet

Using C = 5600/11, we get
radius, r = 81 feet approx

(-81 , 0) is the initial position of George.

So, George's position is given by
(81cost , 81sint), initially, t = pi

Now, 1920 / (5600/11) is 132/35
which is 3 27/35....

We are interested only in the remaining 27/35th of the circumference that was covered....

27/35th of 360 = 277.7142857142857143 degrees in clockwise

So, we have :

(81cost , 81sint)

The horizontal distance is
81*cos(277.7142857142857143) = -10.872894531258

Now, this is 81 + (-10.872894531258)

i.e 70.127105468742

or 70.127 ft eastward ----> ANSWER

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.