When you find a rip in your seam and there's no time to repair it with a sewing machine, you can do it yourself with just a needle and thread. It takes a little more time, but you can sew a sturdy seam by hand that will hold until you can get to a sewing machine.
If you're right-handed, you will be sewing from left to right. If this is uncomfortable for you, sew in the opposite direction.
The seam will be sewn with a backstitch, which is essentially one stitch forward, one stitch back. Starting with the needle under the fabric, make one stitch, then bring the needle up through the fabric one stitch-length (about 1/8 of an inch) beyond the stitch you just made. Then, by stitching backward instead of forward, fill in that blank stitch.
Now for the seam: Using a backstitch and the smallest stitches you can make, bring the needle up through the fabric at the far left point of the seam. Take one or two backstitches, keeping the stitches as small and as even as possible.
Repeat the backstitching across the area to be seamed. If the seam is not sturdy enough, backstitch over the first layer of stitching to reinforce the seam.
For best results, use the same color thread as the fabric, or the closest color as possible. Use doubled thread for the most strength.