SOLUTION: A runner is jogging in a straight line at a steady vr= 2.1 km/hr. When the runner is L= 8.7 km from the finish line, a bird begins flying straight from the runner to the finish

Algebra.Com
Question 1208244: A runner is jogging in a straight line at a
steady vr= 2.1 km/hr. When the runner is
L= 8.7 km from the finish line, a bird begins
flying straight from the runner to the finish
line at vb= 8.4 km/hr (4 times as fast as the
runner). When the bird reaches the finish
line, it turns around and flies directly back to
the runner.
What cumulative distance does the bird
travel? Even though the bird is a dodo, assume that it occupies only one point in space
(a “zero” length bird), travels in a straight
line, and that it can turn without loss of
speed.
Answer in units of km.
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!

Must be a physics class with such ugly numbers.

The runner and bird begin at A. The finish line is C.
It is 8.7 km from A to C.
 
    x          8.7-x
--------------------------
A        B               C 

The runner is at A and runs x km to B in the same time (t) that the bird flies
from A to C to B.  That's 8.7+(8.7-x).

DISTANCE = RATE x TIME
 


Solve the system



Solve that by substitution, get approximately t=1.66, x=3.48

The bird flies 8.7 + 8.7-x = 17.4-3.48 = 13.92 km.

Edwin
RELATED QUESTIONS

A runner is jogging in a straight line at a steady v, 3 km/hr. When the runner is L= 5.9... (answered by ikleyn)
In a 5.00km race, one runner runs at a steady 12.0km/h and another runs at 14.0km/h. how... (answered by ankor@dixie-net.com)
A Cross Country runner ran a race at a speed of 20 km/hr. She ran for 15 minutes (0.25... (answered by josmiceli)
Runner A is initially 5.6 km west of a flagpole and is running with a constant velocity... (answered by ikleyn)
Runner A is initially 5.6 km west of a flagpole and is running with a constant velocity... (answered by ikleyn,greenestamps)
A long-distance runner is running at 5 m/s. How long does it take the runner to travel 1... (answered by stanbon)
runner a is initially 6 km west of a flagpole and is running with a constant velocity of (answered by richwmiller)
Ed is a runner and he runs a 8 km loop every day.The first 4 km, he runs at... (answered by jim_thompson5910)
Hello there! How do I set up this question? one runner passes another runner traveling (answered by richwmiller)