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We report the ${\it Kepler}$ photometry of KIC 11401845 displayingmultiperiodic pulsations, superimposed on binary effects. Light-curve synthesisrepresents that the binary star is a short-period detached system with a verylow mass ratio of $q$ = 0.070 and filling factors of $F_1$ = 45 % and $F_2$ =99 %. Multiple frequency analyses were applied to the light residuals aftersubtracting the synthetic eclipsing curve from the observed data. We detected23 frequencies with signal to noise amplitude ratios larger than 4.0, of whichthe orbital harmonics ($f_4$, $f_6$, $f_9$, $f_{15}$) in the low frequencydomain may originate from tidally excited modes. For the high frequencies of13.7$-$23.8 day$^{-1}$, the period ratios and pulsation constants are in theranges of $P_{\rm pul}/P_{\rm orb}$ = 0.020$-$0.034 and $Q$ = 0.018$-$0.031 d,respectively. These values and the position on the Hertzsprung-Russell diagramdemonstrate that the primary component is a $\delta$ Sct pulsating star. Weexamined the eclipse timing variation of KIC 11401845 from thepulsation-subtracted data and found a delay of 56$\pm$17 s in the arrival timesof the secondary eclipses relative to the primary eclipses. A possibleexplanation of the time shift may be some combination of a light-travel-timedelay of about 34 s and a very small eccentricity of $e \cos {\omega} <$0.0002. This result represents the first measurement of the R{\o}mer delay innon-compact binaries.

KIC 11401845: An Eclipsing Binary with Multiperiodic Pulsations and Light Travel Time