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A alone takes 6 hours more than A+B together. B alone takes 1.5 hours more than A+B together. How long do A and B take together?

1. 3 hours
2. 4 hours
3. 5 hours
4. None of these

Correct answer: 3 hours

Solution

Let T=time together. 1/(T+6)+1/(T+1.5)=1/T. Multiply by T(T+6)(T+1.5): T(T+1.5)+T(T+6)=(T+6)(T+1.5). 2T²+7.5T=T²+7.5T+9. T²=9. T=3 hours.

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