Rational equation word proplem

Question

 Elizabeth drove the first half of the trip at 60 miles per an hour and the rest of the trip at 40 miles per an hour what was the average speed of the whole trip 

Answer 1

When averaging speeds, it is best to be aware of direction for the car. In this problem, the average speed is simply the total distance divided by the total time.

speed = d/T

Rearranging the time of travel is the distance divided by the speed:

T = d/speed

To find the total distance, define a distance D miles that she travels. For distance D/2, she goes at a speed of 60 miles per hour. So the time traveled is:

T1 = (D/2) / 60MPH = D/120 hr.

For the second half, she travels a distance of D/2 at a speed of 40 miles per hour. So the time traveled is:

T2 = (D/2) / 40MPH = D/80 hr.

Therefore, the total time of travel is:

T1 + T2 = D(1/120 + 1/80) = D/48 hr. And the total distance is D miles. Thus:

Speed = D/(D/48) = 48 MPH