Greg the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the ot
her (not both). On Wednesday there were 3 clients who did Plan A and 5 who did Plan B. On Thursday there were 9 clients who did Plan A and 7 who did Plan B. Greg trained his Wednesday clients for a total of 6 hours and his Thursday clients for a total of 12 hours. How long does each of the workout plans last?
This problem can be solved by algebraic method. Let x = the total time spent of all clients in Plan A y = the total time spent of all clients in Plan B We represent two variables x and y because there are two plans that won't be happened simultaneously. On Wednesday, the two workout plans have the total time of 6 hours. We equate 3x + 5y = 6 While on Thursday, the total time is 12 hours. We also equate 9x + 7y = 12
To find x and y, we can use the substitution method. For the first equation, we arrange it in terms of y, that is 5y = 6 - 3x y = (6 - 3x)/5
Substitute it to the second equation: 9x + (7/5)(6 - 3x) = 12 9x + (42/5) - (21/5)x = 12 Multiply the equation by 5 to cancel the denominator: 45x + 42 - 21x = 60 45x - 21x = 60 - 42 24x = 18 x = 18/24 = 3/4 hours
For y: 3(3/4) + 5y = 6 9/4 + 5y = 6 Multiply the equation by 4 to cancel the denominator: 9 + 20y = 24 20y = 24 - 9 20y = 15 y = 15/20 = 3/4 hours
Hence, each workout plans are done within 3/4 hours (or 45 minutes).
