Multiple$-$Concept Example $4$ presents one method for modeling this type of problem. Civil engineers use a transit theodolite when surveying. A modern version of this device determines the distance by measuring the time required for an ultrasonic pulse to reach a target, reflect from it$,$ and return. Effectively, such a theodolite is calibrated properly when it is programmed with the speed of sound appropriate for the ambient air temperature. $($a$)$ Suppose the roundtrip time for the pulse is $0\mathrm{.}341$ s on a day when the air temperature is $293$ K $,$ the temperature for which the instrument is calibrated. How far is the target from the theodolite? $($b$)$ Assume that air behaves as an ideal gas. If the air temperature were $303$ K $,$ rather than the calibration temperature of $293$ K $,$ what percentage error would there be in the distance measured by the theodolite? Give your answer as a number between zero and one hundred with no units.

$($a$)$ Number $$ Units

$($b$)$ Number $$ Units