Question

two cars are 120 mi apart and travel toward each other along the same road. they meet in 2 hours one car travel 6 mph faster than the other car. what is the average speed of each car

Answer 1

Speed of Car 1: C1

Speed of Car 2: C2

Distance between Car 1 and Car 2: 120 mi

Time to meet: 2 hours

distance is equal to speed multiplied by time

`\begin{gathered} 120=C_1t+C_2t \\ \\ t=2h \\ \\ 120=t(C_1+C_2) \end{gathered}`

Car 1 travels 6mph faster than Car 2:

`C_1=C_2+6\text{mph}`

Use the next system of equations:

`\begin{gathered} 120=t(C_1+C_2)_{} \\ C_1=C_2+6 \end{gathered}`

To solve:

1. Substitute the value of C1 in the first equation ofr the given in the second: t=2

`120=2(C_2+6+C_2)`

2. Solve for C2:

`\begin{gathered} 120=2(2C_2+6) \\ 120=4C_2+12 \\ 120-12=4C_2 \\ 108=4C_2 \\ (108)/(4)=C_2 \\ \\ C_2=27 \end{gathered}`

3. Use the value of C2 to find C1:

`\begin{gathered} C_1=C_2+6 \\ C_1=27+6 \\ \\ C_|=33 \end{gathered}`Then, the average spped of car 1 is 33mph and average spped of car 2 is 27mph