Question

2 girls live 3 miles apart on the same road. If they walk towards each other at rates that differ by 1/2 mph and meet exactly 24 minutes later, how fast was each girl walking?

Answer 1

How fast is Girl #1 Walking? Is she the faster or the slower?

Give her speed a name, please.

Answer 2

I don't know how fast Girl#1 is walking, but she is going 1/2 mph slower than girl#2.

Answer 3

Good. Girl #2 is the faster. That is an important choice. It doesn't matter which one, but you do have to pick on in order to stay organized?

You did not give the NAME of the Speed of Girl #1. It is quite laborious to call it "Speed of Girl #1". We need something more convenient. What shall it be?

Answer 4

You can just use x and y

Answer 5

There's a reason why I asked for only the speed of Girl #1. We could use x and y, but this might be excessive.

If the speed of Girl #1 is x mph,
Then the speed of Girl #2 is (x+1/2) mph.

Do you agree with this assessment?

Answer 6

ok

Answer 7

How long did they walk?

Answer 8

For 24 minutes

Answer 9

We have Distance = Rate * Time. We're going to want "Rate * Time". Can we do that without any trouble or do you see a small problem?

Answer 10

minutes and hours

Answer 11

Oh, you're good!!! We need to convert minutes to hours, since our speeds are defined in terms of hours.

24 min = What hours?

Answer 12

.4 or 2/5

Answer 13

Perfect. We are now ready to solve the problem.

Distance = 3 miles
It's in the problem statement.

Rate = (x)+(x+(1/2)) mph
Since they are walking directly towards each other, we can just add them.

Time = (2/5) hour
This is sort of in the problem statement. We did have to translate it a little.

Solve!!

Answer 14

I don't understand this

Answer 15

Do we have the formula Distance = Rate * Time? Do you understand how that works?

Answer 16

yes

Answer 17

The fundamental idea is that if we have any two of these items, we can solve for the third.

If we have Distance and Rate, we can use division and solve for Time.
If we have Distance and Time, we can use division and solve for Rate.
If we have Rate and Time, we can use multiplication to solve for Distance.

Still with me?

Answer 18

yes

Answer 19

The problem statement gave us the time (24 min = 4/5 hours) and the distance (3 miles).

Use this information to calculate the total speed.

Answer 20

2.4

Answer 21

Try again. Distance = Rate * Time

3 miles = Rate * (4/5 hour)

Rate = (3 miles) / (4/5 hour) = (3 / (4/5)) miles/hour = (3 * 5/4) mph = 3.75 mph

Agreed?

Answer 22

yes

Answer 23

The TOTAL speed is 3.75 mph

One is walking at x mph
The other is walking at x + ½ mph

Using this 'x' that we have defined, what is the total speed?

Answer 24

so the slower person would be going 3.5 mph, and the faster would be going 4 mph.

Answer 25

thank you

Answer 26

No, that's not it. The total speed would then by 7.5 mph. That's no good. We alredy know the total speed is 3.75 mph.

Thus, x + (x + ½) = 3.75

You must solve this for 'x'!

Answer 27

all I needed to know was how fast each girl was going. and it was right.

Answer 28

... not if it accepted 3.5 and 4.

Answer 29

* Correction. I'm not sure how it changed from 2/5 to 4/5. Missed a reasonableness check, somewhere.

3/(2/5) = 15/2 = 7.5 and we DO have 3.5 and 4.0. Not sure how the OP got there.