Find Total Work and Daily Rates

Assume total work is the LCM of 10 and 15, which is $30$ units. P's 1-day work is $\frac{30}{10} = 3$ units/day and Q's 1-day work is $\frac{30}{15} = 2$ units/day.

$\text{LCM}(10, 15) = 30$

Calculate Work Done Together

Combined 1-day work of P and Q is $3 + 2 = 5$ units/day. In 3 days, they complete $5 \times 3 = 15$ units of work.

$W_{\text{done}} = (3 + 2) \times 3 = 15$

Determine Remaining Work

Subtract the work done from the total work to find the remaining work: $30 - 15 = 15$ units.

$W_{\text{rem}} = 30 - 15 = 15$

Calculate Days Needed by P

Since Q leaves, P completes the remaining 15 units alone at a rate of 3 units/day, taking $\frac{15}{3} = 5$ days.

$T = \frac{15}{3} = 5$