How Can Julie Determine Her Average Speed on Her Return Trip?

[lawsonj]

Homework Statement

"Julie drives 100 mi to her Grandmother's house. On the way, she drives half the distance at 40 mph and half the distance at 60 mph. On her return trip, she drives half the time at 40 mph and half the time at 60 mph."

Homework Equations

a. "What is Julies average speed on the way to Grandmother's house?"
b. "What is her average speed on the return trip?"

The Attempt at a Solution

The book says a. is 48 m/h and b. is 50 m/h...but i don't exactly know how this was found.

I am thrown by the second question BC 1. How could she possibly know what "half the time" is if she doesn't know her average velocity? 2. how do you find delta-t from this information?

By working out delta-t from the first question, I figured that the trip (50% 40 m/h & 50% 60 m/h) took 2.083 hrs total, which would make 1/2delta-t = 1.0417 hr. This is as close as I could get to determining HOW to find 1/2delta-t in order to calculate what her av. speed is traveling "half the time" at 60 and half the time at 40.

my instinct says that the answer to a. is 50 m/h but the book says otherwise...
how do you find the answer to b. without knowing delta-t?

please help, sincerely,
someone bad at math

 

[Vitaliy]

First thing first, what is the equation for avg speed? Both parts are simple substitution problems.

For part a, you know how long it takes to travel half the distance @ 40mph and how long it takes to travel half the distance @ 60mph. You have time and distance right there.

For part b, you solve for time. How do you solve for time when you have speed and total distance? Use total distance, time, and speed to set up an equation you can solve for time. Use the units as a hint if you are not sure how to setup an equation for time. For example mph * hours = miles. Or miles / mph = hours

 

[SteamKing]

Homework Statement

"Julie drives 100 mi to her Grandmother's house. On the way, she drives half the distance at 40 mph and half the distance at 60 mph. On her return trip, she drives half the time at 40 mph and half the time at 60 mph."

Homework Equations

a. "What is Julies average speed on the way to Grandmother's house?"
b. "What is her average speed on the return trip?"

The Attempt at a Solution

The book says a. is 48 m/h and b. is 50 m/h...but i don't exactly know how this was found.

I am thrown by the second question BC 1. How could she possibly know what "half the time" is if she doesn't know her average velocity? 2. how do you find delta-t from this information?

By working out delta-t from the first question, I figured that the trip (50% 40 m/h & 50% 60 m/h) took 2.083 hrs total, which would make 1/2delta-t = 1.0417 hr. This is as close as I could get to determining HOW to find 1/2delta-t in order to calculate what her av. speed is traveling "half the time" at 60 and half the time at 40.

my instinct says that the answer to a. is 50 m/h but the book says otherwise...
how do you find the answer to b. without knowing delta-t?

please help, sincerely,
someone bad at math

Since the total distance which Julie traveled is still 100 miles, you assume that the total return trip time is x hours. You know that Julie spends x/2 hours driving at 40 mph and x/2 hours at 60 mph. Calculating the total distance from those two pieces of information must add up to 100 miles. That's how you find x.

 

[lawsonj]

thanks gang, i think i figured it out...

on a conceptual note...am I wrong that Julie would not know what "half the time" is going to be? On her trip TO grandma's house, she knew the distance was 100 mi, but the time it took her to get there depended on how long she was traveling at 40 or 60 mph. Therefore, since she is NOT traveling half the distance at each speed any longer, she would not know what "half the time" of her trip is going to be, since the distance she spends at each speed is still unknown?

 

[SteamKing]

thanks gang, i think i figured it out...

on a conceptual note...am I wrong that Julie would not know what "half the time" is going to be? On her trip TO grandma's house, she knew the distance was 100 mi, but the time it took her to get there depended on how long she was traveling at 40 or 60 mph. Therefore, since she is NOT traveling half the distance at each speed any longer, she would not know what "half the time" of her trip is going to be, since the distance she spends at each speed is still unknown?

No, you are not wrong. Sometimes, HW problems are poorly crafted. Still, overlooking some obvious inanities in their construction, a solution to such problems can be obtained by not obsessing over the details.