RATIONAL EQUATION: APPLICATIONS & PROBLEM SOLVING

Transcription

1 RATIONAL EQUATION: APPLICATIONS & PROBLEM SOLVING When finding the LCD of problem involving the ddition or subtrction of frctions, it my be necessry to fctor some denomintors to discover some restricted vlues, tht is vlues tht if used mke the denomintor of one or more of the frctionl terms zero. Exmple. Solve Step. Fctor the denomintors nd find the LCD. ( )( ) 2 LCD ( ) ( ) ± Step 2. Multiply ll terms by the LCD. ( )( ) ( )( ) ( )( 2 ) ( )( ) ( )( ) ( )( ) ( )( 2 ) Step. Simplify. ( )( ) ( )( ) ( )( ) ( )( 2 ) ( ) ( ) [ ] ( ) 2 [ ] Mth002 Student Lerning Assistnce Center - Sn Antonio College

2 Mth002 Step. Solve for Exmple 2. Solve 2 for p. p p 2 p 2 2 p Step. Find the LCD nd restricted vlues. LCD (p) ( p 2 ) p 0, 2 Step 2. Multiply ll terms by the LCD. 2 p p 2 p 2p ( p)( p 2) ( p)( p 2) 2 2 p Step. Simplify. p 2 p 2p ( p)( p 2) ( p)( p 2) ( p)( p 2) 2 ( 2 ) ( p 2 ) - [ ( ) ( p ) ] - 2p p - - p - Step. Solve for p. - p p - p - - p - - p - p This is the solution since this vlue ws not restricted nd the check works. Using the principles covered, it is now possible to solve for single unknown in formul. Student Lerning Assistnce Center - Sn Antonio College 2

3 Mth002 Exmple. Solve I ne for n. R nr Step. Alter the formul so tht there re no frctions. To do this multiply both sides by the denomintor. ne I R nr ( R nr) ( R nr) RI nri ne Step 2. Group together ll terms tht contin the vrible to be solved. RI nri ne RI nri nri ne nri RI ne nri Step. Fctor out the vrible to be solved. RI ne nri RI n ( E ri ) Step. Isolte n. RI n ( E ri ) RI E ri ( E ri ) ( E ri ) n RI E ri n This is the solution becuse there is only one of the vribles, n, tht ws to be solved for. Problems involving uniform motion nd time my lso be solved using these techniques. Student Lerning Assistnce Center - Sn Antonio College

4 Mth002 Exmple. Frnk cn clen certin vcnt lot in 7 hours while Sue cn do it in 5 hours. How long will it tke them both to clen the lot? Step. Orgnize the dt nd crete formul..) b.) c.) d.) Let x represent the number of hours it tkes both to do the tsk. Frnk completes of the job n hour. 7 Sue completes of the job n hour. 5 Together they complete of the job n hour. x Therefore: The prt done by Frnk The prt done by Sue The whole job is 7 5 x Step 2. Find the LCD nd restrictions. LCD 7 * 5 * x 5x x 0 Step. Multiply ll terms by the LCD nd simplify. 5 x 7 5 5x x 5 x 5x 7 5 5x 7x 5 2x 5 5x x Step. Solve for x nd convert. 2x 5 2 x x hours. hours 2 hours Since 2 hour is 5 minutes the totl converted time would be 2 hours nd 55 minutes. Student Lerning Assistnce Center - Sn Antonio College

5 Mth002 Exmple 5. Gerld drives 00 miles est to Houston. He verges 70 miles per hour on the interstte, but while going through Speed Trp County he reduces his speed to 55 miles per hour. If the trip tkes 5 hours how mny miles of the rod were in Speed Trp County? Step. Orgnize the dt..) Let x represent the number of miles in Speed Trp County (t reduced speed). b.) The blnce of the miles driven t 70 mph would be 00 x. Step 2. Determine the formul to be used to solve the problem. The formul D RT, where D distnce, R rte nd T time, will be used. Since the time is wht is unknown, the eqution is ltered to solve for T. D RT D R RT R D T R Step. Substitute the vlues found for the formul vribles. Loction D R T Outside of Speed Trp County 00 x x 70 Inside of Speed Trp County x 55 x 55 Step. Crete the formul to solve the problem. Since the Time t 70 mph Time t 60 mph 5 hours ( totl trvel time) The formul is 00 x x 5 hours Student Lerning Assistnce Center - Sn Antonio College 5

6 Mth002 Step 5 Find the LCD nd multiply ll terms by it. LCD 2 * 5 * 7 * x x ( 5 ) x x ( 5 ) Step 6. Simplify. ( 00 x ) ( x ) x x x x x 550 Step 7. Solve for x. x 550 x 550 x 8 miles. Student Lerning Assistnce Center - Sn Antonio College 6