document.write( "Question 1139968: Two buses are driving along parallel freeways that are 5𝑚𝑖 apart, one heading east and the other heading west. Assuming that each bus drives a constant 55𝑚𝑝ℎ, find the rate at which the distance between the buses is changing when they are 13𝑚𝑖 part, heading toward each other. \n" ); document.write( "
Algebra.Com's Answer #760643 by KMST(5328)\"\" \"About 
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If we count time from the moment the buses are approaching each other but still 13 miles apart, the distance \"D\" (in miles) between the buses as a function of time \"t\" (in hours) is
\n" ); document.write( "\"d=f%28t%29=sqrt%28%2813-110t%29%5E2%2B5%5E2%29\"
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\n" ); document.write( "As the buses are passing each other, their distance is about 5 miles, and not changing very sharply. When they are very far from each other their distance is changing by almost 110mph. At a time \"t\" , the rate of change (in mph) for the distance between the buses is the value of the derivative of the function \"f%28t%29\" above.
\n" ); document.write( "That derivative, \"df%2Fdt\" or \"%22f%27%22\" is the function
\n" ); document.write( "\"%22f+%27+%28+t+%29%22=-110%2813-110t%29%2Fsqrt%28%2813-110t%29%5E2%2B5%5E2%29\" , and its value at \"t=0\" is
\n" ); document.write( "\"%22f+%27+%28+0+%29%22=-110%2813%29%2Fsqrt%2813%5E2%2B5%5E2%29=-1430%2Fsqrt%28194%29\" .
\n" ); document.write( "It is a negative value, because the distance is decreasing, and in absolute value is approximately \"102.66\" .
\n" ); document.write( "When the buses are at 13 miles from each other, approaching each other, the distance between them is decreasing at \"highlight%28approximately+102.66mph%29\" . \n" ); document.write( "
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