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Outside a sweet shop, its name "Madhu Sweet House" is displayed using blinking lights. Each word flashes at a regular interval and remains lit for $1$ second. After remaining lit for $1$ second, "Madhu" remains unlit for  $3 \dfrac{1}{2}$ seconds, "Sweet" remains unlit for $5 \dfrac{3}{4}$ seconds and "House" remains until $9\frac{1}{8}$ seconds. If all the words flash together at $8:00$ p.m. sharp, find the time interval between the next time the first two words flash together and the next time the last two words flash together

1. $45$ seconds
2. $22.5$ seconds
3. $112$ seconds
4. $6.75$ seconds

1