Working alone

Tom and Chandri are doing household chores. Chandri can do the work twice as fast as Tom. If they work together, they can finish the work in 5 hours. How long does it take Tom working alone to do the same work?

Result

T =  15 h

Solution:

C=T/2  5(1/C+1/T)=1 5(2/T+1/T)=1 5⋅ 3/T=1 T=5⋅ 3=15 h=15 h  C=T/2=15/2=152=7.5 h  x=5⋅ (1/C+1/T)=5⋅ (1/7.5+1/15)=1 x=1C=T/2 \ \\ \ \\ 5(1/C + 1/T)=1 \ \\ 5(2/T + 1/T)=1 \ \\ 5 \cdot \ 3/T=1 \ \\ T=5 \cdot \ 3=15 \ \text{h}=15 \ \text{h} \ \\ \ \\ C=T/2=15/2=\dfrac{ 15 }{ 2 }=7.5 \ \text{h} \ \\ \ \\ x=5 \cdot \ (1/C + 1/T)=5 \cdot \ (1/7.5 + 1/15)=1 \ \\ x=1

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