How much time and distance is covered on a trip with varying speeds?

[balling12]

Homework Statement

A person takes a trip, driving with a constant speed of 91.0 km/h except for a 22.0 min rest stop. If the person's average speed is 62.4 km/h, how much time is spent on the trip and how far does the person travel?

Homework Equations

The Attempt at a Solution

not sure how to begin

 

[cepheid]

You haven't put anything under the relevant equations. The problem asks you to deduce distance traveled and time spent based on an average speed. What is the definition of average speed?

 

[dx]

Let T be the total time that he drives (not including the rest stop), and D the total distance that he travels. You know that D/T = 91 km/h. That's one equation.

What is the average speed in terms of D and T? This will be your second equation.

You can solve these two equations for D.

 

[balling12]

average speed= total distance/total time

 

[cepheid]

Right, and how does the total time relate to the time that he drives (which is T using dx's notation)?

 

[balling12]

T-22 minutes?

 

[cepheid]

T-22 minutes?

Why subtraction? Are you saying that the total time for the trip is LESS than the time spent driving?

If I spend T minutes driving *and* 22 minutes sitting at a rest stop, what is the total time I spend on the trip?

 

[balling12]

ok so it would be the total time(T)+22. sorry i got that confused. But i am still unsure were to go from there?

 

[cepheid]

ok so it would be the total time(T)+22. sorry i got that confused. But i am still unsure were to go from there?

Remember that you have two equations and two unknowns. The unknowns are:

distance traveled (D)

time spent driving (T)

The two equations are:

driving speed = 91 km/h = distance driven/time spent driving = D/T

average speed (by *definition*) = 64 km/h = distance traveled / TOTAL time = D/(T+22)

Two equations, two unknowns. This means that you can get a unique solution for both D and T.

 

[cepheid]

Here are the equations more cleanly:

91 = D/T

64 = D/(T+22)

 

[dx]

It's better to write 22 minutes as 22/60 hours to keep the units consistent. Then you will get the answers for D and T in kilometers and hours respectively.