d = distance
v = rate/speed
t = time
we have bus 1, with v1
and
bus 2, with v2
[tex]\begin{gathered} d=v\cdot t \\ d=d_1+d_2 \\ 288=d_1+d_2 \\ 288=v_1\cdot2+v_2\cdot2 \\ we\text{ also know that: } \\ v_1=v_2-14 \\ \text{Then: } \\ 288=(v_2-14)_{}\cdot2+v_2\cdot2 \\ 288=2v_2-28+2v_2 \\ 288+28=4v_2 \\ 316=4v_2 \\ \frac{316}{4}=v_2 \\ v_2=79\text{ mi/h} \\ \\ v_1=v_2-14 \\ v_1=79-14 \\ v_1=65\text{ mi/h} \end{gathered}[/tex]