Question

lucy drove from her house to a friends house at an average speed of 40 miles per hour. she returned home along the same route at an average speed of 60 miles per hour. If her total driving time was 1 hour, how many total miles did lucy drive?

Answer 1

She drove 40 mph for \(x\) hours, and 60 mph for \(1-x\) hours. In that time, she drove the same distance:

\[40 x = 60(1-x)\]Solve that for \(x\) to find out how long she drove at 40 mph. \(1-x\) gives you the driving time at 60 mph. Multiply speed * time to get distance for each leg.

Answer 2

so after i multply that, thats the answer?

Answer 3

One step at a time. Find the value of \(x\).

Answer 4

x=3/5

Answer 5

very good! So she drives for 3/5 of an hour at 40 mph on the trip to her friends house. How far away does her friend live?

Answer 6

24

Answer 7

miles away?

Answer 8

Right. And after visiting her friend, she drives back home along the same route. How much total driving does she do? Yes, units are miles because the speeds were in miles/hour and the time was in hours

Answer 9

60 miles/hour

Answer 10

Let me rephrase my question: "how many miles did she drive?"

Answer 11

from her friends house to her house?

Answer 12

Reread the problem statement. What are you asked to find?

Answer 13

Essential skill in solving problems: know what you are trying to find!

Answer 14

trying to find what is the total miles lucy drives

Answer 15

Okay. So, the answer is?

Answer 16

60 miles

Answer 17

Show me how you arrived at that figure.

Answer 18

so like at first you get x=3/5 and then 3/5 multiplied by 40= 24 and then 3/5*60=36 so then 36+24=60

Answer 19

No. \(x\) represents the number of hours she drove on the way to her friend's house, traveling at 40 mph. It does NOT represent the number of hours she drove at 60 mph on the return trip along the same route.

Answer 20

oh

Answer 21

Stop. Read the problem carefully. Think. Do not use any numbers until you see your mistake.

Answer 22

idk what i did wrong, idk why i keep getting 60

Answer 23

"She drove 40 mph for x hours, and 60 mph for 1−x hours. "

Answer 24

But even more fundamentally: "she returned home along the same route"

Answer 25

If she takes the same route, isn't the distance going to be the same?!?

Answer 26

yea but the time isnt the same

Answer 27

BFD. We want to know HOW MANY MILES SHE DROVE

Answer 28

We know that she drove 24 miles on the way to her friend's house. She drove the same route on the way home. How many miles did she drive in total?

Answer 29

48

Answer 30

YES!!!!

Answer 31

You could also calculate it. \((1-x)\) is the number of hours she spent driving home, at 60 mph. Remember, the total driving time was 1 hour, so if she spent \(x\) driving there, she spent \(1-x\) driving back.

\[(1-\frac{3}{5})*60 =\]

Answer 32

oh, thank you for your help, and im sorry for getting you mad

Answer 33

no, not mad, just frustrated that you couldn't see the end of your nose :-)

Answer 34

Very important to read the problem carefully and understand what you know, and what you need to find. Time spent reading the problem carefully is often more valuable than immediately diving into the calculation...and then when you think you have an answer, read the problem again, and make sure you've answered the right question.

Answer 35

Oh ok thank you :)