37 is the right answer use the network diagram. Item 9 is dependent on both 7 & 8 end result for 7 is 22 so 22 + 15 = 37. Start by item 1 = 0, add 0 to item 2 & 3 duration days because both are dependent are 1. Continue adding the results to items they are dependent on. you will arrive at 37.
If you assign each task with a letter (Task one = A, Task two = B, etc.) you'd see the critical path is
A(1 day)- B (3 days)- D (9 days) -G (10 days) - I (15 days)
1+3+9+10+15 = 38
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