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 #716744 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( "The fastest way to solve this problem is by trial and error, hoping that the speeds are whole numbers.

\n" ); document.write( " $\"258+=+2%2A129+=+2%2A3%2A43\"$
\n" ); document.write( "So a good guess for the first part of the trip is 6 hours at 43 mph.

\n" ); document.write( "That would leave 4 hours for the rest of the trip, which was 208 miles; 208 miles in 4 hours means 52 mph; and indeed 52mph is 9 mph faster than 43 mph.

\n" ); document.write( "Algebraically...

\n" ); document.write( "Let x and x+9 be the two speeds. Then 258 miles at speed x plus 208 miles at speed x+9 makes a total of 10 hours:

\n" ); document.write( " $\"258%2Fx+%2B+208%2F%28x%2B9%29+=+10\"$
\n" ); document.write( " $\"258%28x%2B9%29+%2B+208x+=+10x%28x%2B9%29\"$
\n" ); document.write( " $\"258x+%2B+2322+%2B+208x+=+10x%5E2%2B90x\"$
\n" ); document.write( " $\"10x%5E2+-+370x+-+2580+=+0\"$
\n" ); document.write( " $\"x%5E2+-+37x+-+258+=+0\"$
\n" ); document.write( " $\"%28x-43%29%28x%2B6%29+=+0\"$

\n" ); document.write( "The lower speed is 43 mph; the higher speed is 52 mph.

\n" ); document.write( "Note that in the algebraic solution, we had to factor the quadratic x^2-37x-258; to do that, we had to find two numbers whose product was 258.

\n" ); document.write( "But that's exactly what we did in the first place. So the algebraic solution didn't make the work any easier; it only made us do more work (a LOT more!) to get to the answer. \n" ); document.write( "

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