Question

It takes Joan 6 times longer than Jane to file the reports. ​ Together, they can file the reports in 30 minutes. How long would it take each woman to file the reports by​ herself?

Answer 1

You have to consider the job done = 100% or 1 (100& =1)
let t₁ be the time spent by Joan to complete the 100% of the job AND
let t₂ be the time spent by Jane to complete the 100% of the job
We know that t₁=6t₂ (given),then Joan need 6t₂ to complete the 100% of the job

In 1Minute Joan completes 1/6t₂  (part of the job). In 30 min she competes 30/6t₂ OR 5/t₂
In 1 MINUTE Jane completes 1/t₂ (part of the job).In 30 min she competes 30/t₂
But we know that 5/t₂ +30/t₂ = 1 (100% of the Job)
Reduce same denominator (5/t₂ +30/t₂) = 1/t₂
& t₂ = 35 min needed by Jane to complete the 100% of the job alone &
35 x 6 =210 min (or 3hr & 30 min) needed by Joane to complete the 100% of the job alone

Answer 2

Jane = 35 minutes 
Joan = 210 minutes or 3 hours and 30 minutes