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Two SUVs head toward each other from opposite ends of a freeway 324 miles long. If the speed of the first SUV is 56 miles per hour and the speed of the second SUV is 52 miles per hour, how long will it take before the SUVs pass each other

Respuesta :

3 hours

Explanation

Step 1

let's draw a diagram of the situation

then, Let

time when the Suv pass each other= t

total distance= distance traveled by SUV 1+ distance traveled by SUV2

so

[tex]x+y=324\text{ }\rightarrow equation\text{ (1)}[/tex]

Also, the distance is given by:

[tex]\text{distance}=\text{speed}\cdot\text{time}[/tex]

so, for SUV 1

[tex]\begin{gathered} \text{distance}_1=x=56\cdot t \\ x=56t\rightarrow equation\text{ (2)} \end{gathered}[/tex]

and for SUV2

[tex]\begin{gathered} \text{distance}_2=y=52\cdot t \\ y=52t \end{gathered}[/tex]

so, by replacing x and y values in equation (1)

[tex]\begin{gathered} x+y=324\text{ }\rightarrow equation\text{ (1)} \\ 56t+52t=324 \\ 108t=324 \\ \text{divide both sides by 108} \\ \frac{108t}{108}=\frac{324}{108} \\ t=3 \end{gathered}[/tex]

so, the times is 3 hours

I hope this helps you

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