Sarah rides on a flat road at $10$ kilometers per hour (kph), downhill at $20$ kph, and uphill at $4$ kph. Tom rides on a flat road at $15$ kph, downhill at $25$ kph, and uphill at $6$ kph. Sarah goes from town $X$ to town $Y$, a distance of $12$ km all downhill, then from town $Y$ to town $Z$, a distance of $10$ km all uphill, and then back to town $X$, a distance of $15$ km all flat. Tom goes the other way around using the same route. How many more minutes does it take Sarah to complete the $37$-km ride than it takes Tom?