Question 106551: Two-way radio range:
Two surveyors with two-way radios leave the same point at 9:00AM, one walking due south at 4 mi/hr and the other due west at 3 mi/hr. How long can they communicate with one another if each radio has a maximum range of 2 miles?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Two surveyors with two-way radios leave the same point at 9:00AM, one walking due south at 4 mi/hr and the other due west at 3 mi/hr. How long can they communicate with one another if each radio has a maximum range of 2 miles?
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They cancommunicate until they are 4 miles from one-another
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Draw the picture with one going south at 4mph, the other going west at 3 mph.
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Let the one going west go a distance of "x" miles
Draw a line segment from his position to the postion of the southbound
person. Make the length of that segment be "4"
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Then, using Pythagoras, the distance the southbound person has gon is
sqrt(4^2-x^2) = sqrt(16-x^2) miles.
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EQUATION:
Time = distance/rate
Westbound person time = x/3 hr
southbound person time = [sqrt(16-x^2)]/4
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west time = south time
x/3 = [sqrt(16-x^2)]/4
4x = 3[sqrt(16-x^2)]
Square both sides to get:
16x^2 = 9(16-x^2)
16x^2 = 144 - 9x^2
25x^2 = 144
x = 12/5 = 2.4 miles (distance westbound person goes.
2.4/3 = 0.8 hrs (time the westbound person goes)
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Their maximum communication time is 0.8 hrs. = 48 minutes
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Cheers,
Stan H.
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