LM3914 and LM3915 are dot/bar display drivers used to create basic displays of analog voltage levels. They are widely used in VU-meters and various voltage indicators (for batteries). The LM3914 senses an analog voltage and drives a number of LEDs depending on the level of this voltage. Knowing this, we can provide this voltage from a discharging capacitor. Depending on the resistive load which discharges the capacitor, the time required to turn off all LEDs can be set to specific intervals. This is how a timer is made using LM3914 (or LM3915).
This IC contains a constant current source for LEDs and an adjustable voltage reference. The following circuit uses LM3914 internal current source to charge the capacitor. To be able to modify countdown time, a potentiometer is used to discharge the capacitor. When the last LED is off two opamps drive a relay. The two opamps are part of the LM358 integrated circuit and one of them is used, in a similar manner, with a capacitor that is charged/discharged to provide an optional turn-off time for the relay. By setting a jumper you can choose between relay always on after time is up or relay on for an adjustable amount of time.

LM3914 countdown timer built on PCB