Question

A team of three students are working on a language-learning app; they need to develop 300 micro-lessons and 300 micro-tests before they can make their first release. Jordan can develop 10 lessons and 5 tests in a day; Marco can develop 5 lessons and 10 tests in a day; Junyi can develop 5 lessons and 8 tests in a day.

(a) Write a system of equations that can be used to determine how long each team member must work to develop exactly 300 lessons and 300 tests.
(b) Find the general solution to the system from (a).
(c) Find the specific solutions if
(i) Junyi gets sick, so can not work;
(ii) Jordan gets a part-time job, and so can only work 10 hours.

Answer 1

Answer: a) 15 b)

Explanation:

Let X be the number of days:

a)

For LESSONS:

Jordan does 10 / day ( 10*X)

Marco 5 / day ( 5*X)

Junyi 5 / day ( 5*X)

For TESTS:

Jordan does 5 / day ( 5*X)

Marco 10 / day ( 10*X)

Junyi 8 / day ( 8*X)

for each they need a total of 300

a)
`10X+5X+5X=300 => 20X = 300 => X = 15` days for the lessons

b)
`5X+10X+8X = 300 => 23X = 300 => X = 13.04` days for the tests

so they need 15 days to finish both tasks

now if Junyi gets sick we just eliminate his contribution

a)
`10X+5X=300 => 15X = 300 => X = 20` days for the lessons

b)
`5X+10X = 300 => 15X = 300 => X = 20` days for the tests

so in 20 days they will finish without him

If jordan works 10 hours a day, we just replace him with 10/24

a)
`10(10/24)+5X+5X= 300 => X = 29.58` days for the lessons

b)
`5(10/24)+10X+8X = 300 => X = 16.51` days for the tests

so at the end to complete both tasks they need 29.58 days