Two cars traveling toward each other are 210 miles apart. Car A is traveling 10 miles per hour faster than car B. The cars pass after 3 hours. How fast is each car traveling?

Solution

- The solution steps are given below:

$\begin{gathered} \text{ Let the speed of car A be }V_A \\ \text{ Let the speed of car B be }V_B \\ \\ \text{ Let the distance covered by car A be }X_A \\ \text{ Let the distance covered by car B be }X_B \\ \\ \text{ Both cars reach each other at the same time. Let that time be }t \\ \text{ This means that using the distance-speed-time formula, we have:} \\ X_A=V_At\text{ \lparen Equation 1\rparen} \\ \\ X_B=V_Bt\text{ \lparen Equation 2\rparen} \\ \\ \text{ Since both cars covered a combined distance of 210 miles before they could cross each other, we have:} \\ X_A+X_B=210\text{ \lparen Equation 3\rparen} \\ \\ \text{ Also, we know that car A is 10mph faster than car B} \\ V_A=V_B+10\text{ \lparen Equation 4\rparen} \\ \\ \text{ Substitute Equation 4 into Equation 1} \\ X_A=(V_B+10)t \\ \text{ But we know that }t=3\text{ hours} \\ X_A=(V_B+10)*3=3V_B+30\text{ \lparen Equation 5\rparen} \\ \\ Substitute\text{ Equations 2 and 5 into Equation 3} \\ (3V_B+30)+V_Bt=210 \\ 3V_B+30+3V_B=210 \\ \text{ Subtract 30 from both sides} \\ 6V_B=210-30=180 \\ \text{ Divide both sides by 6} \\ \\ V_B=(180)/(6)=30mph \\ \\ V_A=V_B+10 \\ \\ V_A=30+10 \\ V_A=40mph \end{gathered}$

Final Answer

- The speed of car A is 40 mph

- The speed of car B is 30 mph

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Two cars traveling toward each other are 210 miles apart. Car A is traveling 10 miles per hour faster than car B. The cars pass after 3 hours. How fast is each car traveling?

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