In a 12-hour period of time, a drawbridge opens 8 times, holding traffic for 15 minutes each time. If a car approaches the bridge during this 12-hour time, find the probably the The bridge is open!!

Step-by-step explanation:

You only need two equations for this problem. First determine variables:

h represents height

R represents rate of rise

t represents time needed to reach the full height

Note that R will be expressed as a measure of distance over minutes, for instance meters per minute, and h will be expressed in units of distance, such as meters. t is expressed in minutes.

The equations needed are as follows:

(3/2)min * R= (6/20) h

{One and a half minutes times rate of rise equals six twentieths of full height. When you multiply minutes by rate of rise, the minutes divide out leaving a distance unit}

t = h/R

{Time to reach full height equals full height divided by rate of rise. When you divide the height, expressed in distance, by the rate, expressed in distance over time, the distance units divide out leaving a time unit}

It is not necessary to know either R or h since they will divide out when you solve for t.

First, solve for h in the first equation.

Then, take the answer from that and substitute it for h in the second equation.

This will produce an equation that will reduce to a known t value.

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David W. answered • 12/28/15

TUTOR 4.5 (50)

Experienced Prof

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The key clue is "at a constant rate." That means that rate = (distance)/(time) is always the same, so we can set them equal.

rate given = total rate

(1 1/2 minutes) / (6/20 d) = (t minutes) / (1 d) [t=time; d=total height of drawbridge]

t = ( (1 1/2 minutes) / (6/20 d) ) (1 d) [multiply both sides by 1 d; reverse equals]

t = (1 1/2) / (6/20) minutes [d cancels out, leaving only minutes]

t = (3/2) ( 20/6) minutes [convert to improper fraction; to divide by fraction, invert and multiply]

t = 5 minutes

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