Gardener (g) only = 6.5 working hours
Gardener (g) + Helper (h) = 5 working hours
Without the helper, the gardener does 6.5 hours
With a helper, the gardener saves 1.5 hours meaning the helper uses 1.5 hours to fully assist the gardener working
T = 6.5 hours
Gardener completes 2/13 of the job in one hour.
Gardener + helper = 1.5 hours less than 6.5 = 1 / 5 of the job in one hour
To obtain effort of the helper alone every hour, we subtract the time the gardener alone takes to complete the job every hour by the time they both take to complete the job every hour.
-> (1 / 5) - (2 / 13)
-> [(1 * 13) - (5 * 2)] / (5 * 13)
-> (13 - 10) / 65
-> 3 / 65
• 3/65 is the time spent by the helper each hour
• So to find how long it will take for the helper to do the job himself, we get the reciprocal of 3/65
-> 1 / (3/65)
-> 65/3
Hence, the time taken for the helper to do the job alone is 21.67 hours
