document.write( "Question 1102120: Greg drove at a constant speed in a rainstorm for 258 miles. He took a​ break, and the rain stopped He then drove 208 miles at a speed that was 9 miles per hour faster than his previous speed. If he drove for 10 ​hours, find the​ car's speed for each part of the trip. THANK YOU!! \n" ); document.write( "
Algebra.Com's Answer #716743 by htmentor(1343)\"\" \"About 
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Let s = the speed and t = the time for the first part of the trip
\n" ); document.write( "Then s + 9 is the speed for the second part of the trip
\n" ); document.write( "The total time is 10 h, so the time for the second leg is 10 - t
\n" ); document.write( "For the first leg of the trip s = 258/t -> t = 258/s [1]
\n" ); document.write( "For the second leg, s + 9 = 208/(10 - t) [2]
\n" ); document.write( "We have two equations and two unknowns
\n" ); document.write( "Substitute [1] into [2]:
\n" ); document.write( "s + 9 = 208/(10 - 258/s) = 208s/(10s - 258)
\n" ); document.write( "(s + 9)(10s - 258) = 208s
\n" ); document.write( "10s^2 - 258s + 90s - 2322 - 208s = 0
\n" ); document.write( "10s^2 - 376s - 2322 = 0
\n" ); document.write( "5s^2 - 188s - 1161 = 0
\n" ); document.write( "This gives s = -5.4 and 43. Only the positive solution is valid.
\n" ); document.write( "Thus the other speed is 43 + 9 = 52
\n" ); document.write( "Ans: 43 mph and 52 mph\r
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