jmc

Since the interest rate is simple, he has to pay an interest of $10\cdot 0.15=1.5$ dollars every day.

Let $x$ be the number of days needed to repay at least double the amount borrowed. Since he has to repay $10aswellas$\$1.5x$ in interest, we have the inequality $10+1.5x\ge 10\cdot 2$. Solving for $x$, we get $x\ge 6.\overline{6}$. The smallest integer greater than $6.\overline{6}$ is $7$. Therefore, it would take at least $\boxed{7\text{ days}}$.