Answer:

Plan A lasts for 1.5 hours

Plan B lasts for 0.5 hours

Step-by-step explanation:

Lena the trainer has two solo workout plans that she offers her clients: Plan A and Plan B

Let x the number of hours that plan A lasts( the time a client takes to complete workout)

Let y = the number of hours that plan B lasts. ( the time a client takes to complete workout)

On Wednesday, there were 12 clients who did Plan A and 2 clients who did Plan B.

This means 12 clients trained for 12x hours under plan A and 2 clients trained for 2y hours under plan B.

On Thursday, there were 3 clients who did Plan A and 5 clients who did Plan B.

This means 3 clients trained for 3x hours under plan A and 5 clients trained for 5y hours under plan B.

Lena trained her Wednesday clients for a total of 19 hours and her Thursday clients for a total of 7 hours.

This means

12x + 2y = 19 - - - - - - - - - - -1

3x + 5y = 7 - - - - - - - - - - -2

Using elimination method,

Multiply equation 1 by 3 and equation 2 by 12

36x + 6y = 57

36x +60y = 84

Subtracting,

54y = 27

y = 27/54 = 0.5 hours per client

Put y = 0.5 in 3x + 5y = 7

3x +5×0.5 = 7

3x + 2.5 = 7

3x = 7-2.5 = 4.5

x = 4.5/3 = 1.5 hours per client