Final answer:
Dorji takes double the time of Dawa to dig a garden, and Dawa takes 2 hours and 30 minutes. Working together, they can dig the entire garden in 1 hour and 40 minutes.
Step-by-step explanation:
The question asks how long it will take Dorji and Dawa to dig a garden together, given that Dorji takes double the time than Dawa. First, we need to convert Dawa's digging time into minutes. Dawa takes 2 hours and 30 minutes, which equals 150 minutes. If Dorji takes double the time, that means he takes 300 minutes to dig the garden by himself.
To find out how long it will take for both of them to dig together, we can think of their work rate in terms of "garden per minute". Dawa digs at a rate of 1/150 garden per minute, and Dorji digs at a rate of 1/300 garden per minute. Working together, their combined rate is (1/150) + (1/300) gardens per minute. This simplified becomes (2/300) + (1/300) = 1/100 garden per minute.
Since they can dig 1/100 of the garden per minute together, they can dig the entire garden in 100 minutes. Converting this back into hours and minutes, that's 1 hour and 40 minutes.
Therefore, Dorji and Dawa digging together will take 1 hour and 40 minutes to finish digging the garden.