Respuesta :
Answer:
84 miles long is the route
Explanation:
Let the distance is d
It is given that driver drove his car with 30 miles per hour
So time [tex]t=\frac{d}{30}[/tex]
And when he return his velocity is 70 miles per hour
So time [tex]t=\frac{d}{370[/tex]
We know that average speed [tex]=\frac{total\ distance}{total\ time}=\frac{2d}{\frac{d}{30}+\frac{d}{70}}=42m/sec[/tex]
Total time of the trip is given as 2 hour
So total distance = total time × average speed = 42×2 = 84 miles
Answer:
The route was 42 miles long.
Explanation:
Let the distance covered from starting point to end point be x.
Average speed of the car = 30 mile/hour
Time taken to cover x distance = t
[tex]t=\frac{x}{30 mile/hr}[/tex]
The distance covered from end point point to starting point back = x
Average speed of the car = 70 mile/hour
Time taken to cover x distance = t'
[tex]t'=\frac{x}{70 mile/hr}[/tex]
Average speed of the car:
[tex]\frac{x+x}{t+t'}=\frac{2x}{\frac{x}{30 mile/hr}+\frac{x}{70 mile/hr}}=42 mile/hour[/tex]
Total time taken in round trip = 2 hours
[tex]\text{Average speed}=\frac{\text{Total distance}}{\text{Total time}}[/tex]
[tex]42 mile/hr=\frac{\text{Total distance}}{2 hr}[/tex]
Total distance covered by car= 42 mile/hr × 2 hr = 84 miles
Distance of the route = 84 ÷ 2 = 42 mile
