$4 \cdot 201$ (1) How much boiling water should be added to $a$ liters of water at $t_{1} \mathrm{C}$ to obtain water at $t_{2} \mathrm{C}$ $\left(t_{1}<100^{\circ} \mathrm{C}\right)$?
(2) If the approximate measured values are:
$a=3.641$ liters, $t_{1}=36.7^{\circ} \mathrm{C}, t_{2}=57.4^{\circ} \mathrm{C}$, how many liters of boiling water should be added?
［Solution］（1）Let the added boiling water be $x$ liters,
then we have $c \cdot x\left(100-t_{2}\right)=c \cdot a\left(t_{2}-t_{1}\right)$ (where $c$ is the specific heat),
so $x=\frac{a\left(t_{2}-t_{1}\right)}{100-t_{2}}$.
(2) When $a=3.641$ liters, $t_{1}=36.7^{\circ} \mathrm{C}, t_{2}=57.4^{\circ} \mathrm{C}$, then $x=\frac{3.641 \times(57.4-36.7)}{100-57.4}=1.769$ (liters).