document.write( "Question 174504: Esther drove to work in the morning at an average speed of 45 miles per hour. She returned home in the evening along the same route and averaged 30 miles per hour. If Esther spent a total of one hour commuting to an from work, how many miles did Esther drive to work in the morning? \n" ); document.write( "

Algebra.Com's Answer #129506 by solver91311(24713) $\"\"$ $\"About$

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Let's say that the time it took her to get to work in the morning is $\"t\"$ hours. Then the time it took her to get home in the afternoon must be $\"1-t\"$ hours. We know that for any trip, distance equals rate times time or $\"d=rt\"$ . That means that the distance she drove to work is given by $\"d=45t\"$ , but we also know that the distance she drove to get home must be the same distance, because she took the same route (and, presumably, no one picked up her house and moved it while she was at work) so for the trip home we can say $\"d=30%281-t%29\"$ and since the distances are equal, we can say:\r
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\n" ); document.write( "\n" ); document.write( " $\"45t=30%281-t%29\"$ → $\"45t=30-30t\"$ → $\"45t+%2B+30t+=+30\"$ → $\"75t=30\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"t=30%2F75=2%2F5\"$ hour to drive to work at 45 mph.\r
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\n" ); document.write( "\n" ); document.write( "Since $\"d=rt\"$ , $\"d=45%2A%282%2F5%29=18\"$ miles \n" ); document.write( "

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