Answer :
Answer:
C. 210 miles
Step-by-step explanation:
We have been given that two cars leave Phoenix and travel along roads 90 degrees apart. Car 1 leaves 30 minutes earlier than Car 2 and averages 42 mph.
We will use distance formula and Pythagoras theorem to solve our given problem.
[tex]\text{Distance}=\text{Speed}\times \text{Time}[/tex]
[tex]\text{Distance covered by Car 1 in 3.5 hours}=\frac{42\text{ Miles}}{\text{Hour}}\times \text{3.5 hour}[/tex]
[tex]\text{Distance covered by Car 1 in 3.5 hours}=147\text{ Miles}[/tex].
Since car 1 leaves 30 minutes before car 2, so car 2 will travel for only 3 hours when car 1 will travel for 3.5 hours.
[tex]\text{Distance covered by Car 2 in 3 hours}=\frac{50\text{ Miles}}{\text{Hour}}\times \text{3 hour}[/tex]
[tex]\text{Distance covered by Car 2 in 3 hours}=150\text{ Miles}[/tex]
Since both car travel along roads 90 degree apart, therefore, the distance between both cars after Car 1 has traveled 3.5 hours would be hypotenuse with legs 147 and 150.
[tex]\text{Distance between both cars}=\sqrt{147^2+150^2}[/tex]
[tex]\text{Distance between both cars}=\sqrt{21609+22500}[/tex]
[tex]\text{Distance between both cars}=\sqrt{44109}[/tex]
[tex]\text{Distance between both cars}=210.021427\approx 210[/tex]
Therefore, the both cars will be 210 miles apart and option C is the correct choice.
