Finding time given average velocity

[canucks81]

Homework Statement

A car travels 120km East at 45km/hr, then goes West 50km at 70km/hr, then goes East again for time t at 40km/hr. If the average velocity for the entire trip is 30km/hr East, find the time t.

Homework Equations

The Attempt at a Solution

time of car traveling East at beginning:
t=d/t 120km/45 kph t = 2.67hr

time of car traveling West
t=d/t 50km/70 kph t = 0.71hr

Now this is where I get stuck. I'm not sure what the next step would be since I'm not given distance for the car traveling East again. The answer is 3.14 hrs. I know a question like this will be on my test tomorrow, so help would be greatly appreciated.

 

[PeterO]

Homework Statement

A car travels 120km East at 45km/hr, then goes West 50km at 70km/hr, then goes East again for time t at 40km/hr. If the average velocity for the entire trip is 30km/hr East, find the time t.

Homework Equations

The Attempt at a Solution

time of car traveling East at beginning:
t=d/t 120km/45 kph t = 2.67hr

time of car traveling West
t=d/t 50km/70 kph t = 0.71hr

Now this is where I get stuck. I'm not sure what the next step would be since I'm not given distance for the car traveling East again. The answer is 3.14 hrs. I know a question like this will be on my test tomorrow, so help would be greatly appreciated.

I would sketch a graph for guidance.

You know how long the vehicle has been traveling for so far, and how far away it currently is. From that can deduce the "other way" of getting there at the right time, just travel 70 km East at a steady speed of (what ever).

Now the graph:

Draw a single line representing an average speed of 30 km/hr, starting at the origin.
Draw a second line from the origin to 70km at time (2.67 + 0.71) hrs.
Now draw a third line, from the end of the second, representing a speed of 40 km/h.

When the 1st and 3rd lines intersect, we have the answer.

You should be able to find the equation of the 1st and 3rd lines and solve algebraically to get the answer you seek.

 

[PeterO]

I would sketch a graph for guidance.

You know how long the vehicle has been traveling for so far, and how far away it currently is. From that can deduce the "other way" of getting there at the right time, just travel 70 km East at a steady speed of (what ever).

Now the graph:

Draw a single line representing an average speed of 30 km/hr, starting at the origin.
Draw a second line from the origin to 70km at time (2.67 + 0.71) hrs.
Now draw a third line, from the end of the second, representing a speed of 40 km/h.

When the 1st and 3rd lines intersect, we have the answer.

You should be able to find the equation of the 1st and 3rd lines and solve algebraically to get the answer you seek.

OR:

Imagine if a second vehicle, traveling at 30km/h East, began at the same time as you. After (2.67 + 0.71) hours, that vehicle will be 30*(2.67 +0.71) km from the start, you are only 120 - 50 km from the start. That shows how far in front the other vehicle would be at that time.
From that time, you are traveling 10 km/hr faster than the first car. How long will it take you to catch up to the other car then?

 

[canucks81]

Thanks for the help, I finally got it.

 

[PeterO]

Thanks for the help, I finally got it.

Note: if you retain the times as fractions [8/3, 5/7] the final answer is 22/7 which you would recognise as the Junior maths approximation of pi, and so 3.14.