Question

Imogene's car traveled 360 miles averaging a certain speed.If the car had gone 5mph faster , the trip would have taken 1 hr less.Find the average speed

Answer 1

360 = vt
360 = (v+6)(t-1)

solve for v

Answer 2

360 = (v+5)(t-1)

typo

Answer 3

If Imogene drives 360 miles at speed \(s\), it takes her t = 360/s to cover the distance.
If she drives the same distance 5 mph faster \((s+5)\), it takes her 1 less hour, or t-1.

We can write two equations:
t = 360/s
t-1 = 360/(s+5)

Substitute the value of t (360/s) from the first equation into the second equation and you're left with an equation only in terms of s. You can solve that for s, which is the speed for the first trip. The speed for the second trip is s+5.

The average speed for the entire trip is miles traveled/total time, or 360*2/(2t-1). You can find t from t = 360/s, once you've found s. The average speed is NOT the average of the two speeds!