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Two buses leave a station at the same time and travel in opposite directions. One bus travels 15 mph faster than the other. If the two buses are 321 miles apart after 3 hours, what is the rate of each bus?

Jan 21, 2020

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Two buses leave a station at the same time and travel in opposite directions.

One bus travels 15 mph faster than the other.

If the two buses are 321 miles apart after 3 hours, what is the rate of each bus?

Formula: $$s=v*t$$

$$\begin{array}{|lrcll|} \hline \text{Bus}_1: & s_1 &=& v_1 *t \\\\ \text{Bus}_2: & s_2 &=& v_2 *t & v_2 = v_1 + 15 \\ & s_2 &=& (v_1 + 15)*t \\ \hline \end{array}$$

$$\begin{array}{|rcll|} \hline s_1+s_2 &=& 321 \\ v_1 *t+(v_1 + 15)*t &=& 321 \\ v_1 *t+v_1*t + 15*t &=& 321 \\ 2*v_1 *t+ 15*t &=& 321 \\ (2v_1 + 15)*t &=& 321 \quad &| \quad t=3~h \\ (2v_1 + 15)*3 &=& 321 \\ 6v_1 + 45 &=& 321 \\ 6v_1 &=& 321 - 45 \\ 6v_1 &=& 276 \quad &| \quad : 6\\ \mathbf{v_1} &=& \mathbf{46~mph} \\\\ v_2 &=& v_1 + 15 \\ v_2 &=& 46+15 \\ \mathbf{v_2} &=& \mathbf{61~mph} \\ \hline \end{array}$$

Jan 21, 2020
edited by heureka  Jan 21, 2020