Question

If a sports car is traveling at 70 miles per hour, how long would it take the sports car to overtake a familycar traveling at 50 miles per hour that left the same starting point 2 hours earlier?hours (if needed, round to two decimalThe sports car would overtake the family car inplaces).

Answer 1

Given,

The speed of the family car, S1=50 miles/h

The speed of the sports car, S2=70 miles/h.

The family car left the starting position t=2 hours earlier.

So, the distance between the family car and the sports car when the sports car starts is,

`\begin{gathered} D=S1* t \\ =50*2 \\ =100\text{ miles} \end{gathered}`

The sports car has to overcome this 100 mile distance to overtake the family car.

The relative speed of sports car with respect to the family car is,

`\begin{gathered} S_(rel)=S2-S1 \\ =70-50 \\ =20\text{ miles/h} \end{gathered}`

So, the time taken by the sports car to overcome the family car is,

`\begin{gathered} t=(D)/(S_(rel)) \\ t=\frac{100\text{ }}{20} \\ t=5\text{ h} \end{gathered}`

Therefoe, the sports car takes 5h to overcome the family car.