Question

Two buses leave towns 288 miles apart at the same time and travel toward each other. One bus travels 14 mi/h slower than the other. If they meet in 2 hours, what is the rate of each bus?

Answer 1

d = distance

v = rate/speed

t = time

we have bus 1, with v1

and

bus 2, with v2

`\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 \\ (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}`