157 1.6 OtherTypes of Equations and Applications Therefore, 1 x = the rate of the faster printer (job per hour) and 1 2x = the rate of the slower printer (job per hour). The time for the printers to do the job together is 2 hr. Multiplying each rate by the time will give the fractional part of the job completed by each. A = rt Rate Time Part of the Job Completed Faster Printer 1 x 2 2A 1 xB = 2 x Slower Printer 1 2x 2 2A 1 2xB = 1 x Step 3 Write an equation. The sum of the two parts of the job completed is 1 because one whole job is done. Part of the job Part of the job done by the + done by the = One whole faster printer slower printer job (111111)111111* (111111)111111* (1111)1111* 2 x + 1 x = 1 Step 4 Solve. xa 2 x + 1 xb = x112 Multiply each side by x, where x ≠0. xa 2 xb + xa 1 xb = x112 Distributive property 2 + 1 = x Multiply. x = 3 Add. Interchange sides. Step 5 State the answer. The faster printer would take 3 hr to do the job alone. The slower printer would take 2132 = 6 hr. Give both answers here. Step 6 Check. The answer is reasonable because the time working together (2 hr, as stated in the problem) is less than the time it would take the faster printer working alone (3 hr, as found in Step 4). S Now Try Exercise 39. NOTE Example 3 can also be solved using the fact that the sum of the rates of the individual printers is equal to their rate working together. Because the printers can complete the job together in 2 hr, their combined rate is 1 2 of the job per hr. 1 x + 1 2x = 1 2 2xa 1 x + 1 2xb = 2xa 1 2b Multiply each side by 2x. 2 + 1 = x Distributive property x = 3 Same solution found earlier
RkJQdWJsaXNoZXIy NjM5ODQ=