Help on Physics question?

Question

A person takes a trip, driving with a constant speed of 89.5 km/h except for a 22 minute rest stop. If the person's average speed is 77.8 km/h, how much time is spent on the trip and how far does the person travel.

Answer 1

You need only one equation to solve this problem: distance = rate * time.  That's all.  You just need to apply it a couple of times.  Let me explain

You don't know the distance yet, but let's call it D.  You don't know the time to get to that distance, so let's call that T.  What you do know is R1 (89.5) and Ravg (77.8).

Now in both cases, with and without the pitstop, the distance is the same, right?  The only difference in the speed and time.

Let's go to our equations.  Equation without the rest stop is easy: D = 77.8 * T

With the rest stop:  D = 89.5 * (T-22/60)

Now, notice that both D's are the same, and that both T's are the same, but I've subtracted 22/60 (I've converted my minutes to hours.. remember to keep units constant, since I'm dealing with km/h in speed) because the time is shorter when I'm going faster.

Now since both D's are the same, I can set the equations equal to each other, and solve for T.

89.5 * (T - 22/60) = 77.8 * T

If you work this out, T = 2.804 hours, or 2 hours and 48.24 minutes.

Now that we have the time, just plug it into either equation (let's use the one without the pit stop to make it easy), and you can find the distance.

D = R*T

D = 77.8 * 2.804 = 218.15 km

Understand?

Hope this helps.

Answer 2

89.5km/h / 77.8km/h = 1.15hrs = 1hr 9min + 22min = 1hr 31min for the trip.

1.15hrs x 89.5km/h = 102.9km travelled.