A person takes a trip, driving with a constant speed of 89.5 km/h, except for a 22.0-min 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? Need solving and explanation. Thanks

Gary S

Let's call the time spent driving t.

Since d=r*t, the distance traveled during that time is

d = 89.5 * t

Meanwhile, average speed is the total distance traveled (which we just computed) divided by total time (which is t + 22 min to account for the rest stop). Since the speed is in km/h, not km/min, we should convert the 22 minutes into hours

22 min*1 hr / 60 min = 0.367 hr

r = d/t
78.8 = 89.5t/(t+0.367)

Rearranging, we get
t + 0.367 = (89.5/78.8)t
t = 0.367/(89.5/78.8 - 1)
t = 2.700 hrs

Remember, t is just the time spent driving, so the total time is t + 0.367 = 3.067 hrs (3 hrs 4 min). The total distance driven is 89.5*2.700 = 241.7 km.

And just to check, the total distance is ALSO the average speed times the total time: 78.8 * (3.067) = 241.7 km. Sure enough - it checks out.

Write down what you know, and you'll come up with a set of equations that you can then solve. Like this:

The distance (D) the person travels is equal to his velocity times time. So he travels at 89.5 Km/h times T hours (T is the time he spends driving, not including the rest stop):

D = 89.5Km/hr * T hr

His average velocity is 77.8 Km/h. This is simply the distance he drove divided by the time he spent doing it, which includes the 22 minute rest stop:

77.8 Km/h = D/(T + 22/60)

Note that you divide 22 min by 60 to get the rest stop time expressed in hours, so that the units work out.

So now you have two equations in two unknowns, and you ought to be able to solve for both D and T. Remember the total time for the trip is T + 22 minutes. Post back if this is still unclear.