Algebraic Story Problem

Fragile Dreams

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Marissa left her apartment at 7:00 AM riding her bike at 12 mi/h. At 7:30 AM Marissa's room-mate Kim realized that Marissa had forgotten her lunch and set off after her, by the same route, riding her moped at 18 mi/h.

(25) Let t = Marissa's travel time. Write an expression for Kim's travel time, using t. Write expressions for Marissa's distance and for Kim's distance, using t.

This entire question and situation has bemused and confounded me. If any one could explain it and how to go about it step-by-step...thanks.
 
Using nicer numbers for the first part:

Kim's speed: 20mi/h
Marissa's speed: 10mi/h

It takes Kim 1 hour to travel 20 miles (because her speed is 20 miles per hour).

It takes Marissa 1 hour to travel 10 miles (because her speed is 10 miles per hour), or 2 hours to travel 20miles.

So Kim has taken 1/2 the time of Marissa to travel the same distance.

Or if t is the time of Marissa in hours, Kim's time is (1/2)t.

See how you go.
 
Okay so:

Write expressions for Marissa's distance and for Kim's distance, using t.

Marissa- 12t = d
Kim- 18t =d
 
But I'm still stumped at this part:

Write an expression for Kim's travel time, using t.

t representing Marissa's travel time

???
 
Kim's speed is 18/12 = 3/2 times faster than Marissa's.

It therefore takes Kim 2/3 of the time of Marissa to travel the same distance.

Hence my first post.
 
The departure times aren't significant because we are talking in terms of the length of time of Marissa's travel.

I may be misreading it but the second part seems odd to me because Kim has to travel the same distance as Marissa to catch up to her.
 
Fragile Dreams said:
So would it essentially be

Marissa: 12t
Kim: 18(t - 1/2)

I would agree that you have written the expressions for the distances traveled by Marissa and Kim. If t represents the time Marissa has traveled by the time Kim catches up with her, then t - 1/2 will represent the time traveled by Kim (Kim left 1/2 hour after Marissa did, so will travel t - (1/2) hours by the time she catches Marissa).

When Kim catches up with Marissa, the two will have traveled the same distance, and
12t = 18[t - (1/2)]
is the equation you can use to find the time t that Marissa has traveled.

Once you know the time traveled by each, you can find the distances too, if necessary.
 
Fragile Dreams said:
So would it essentially be
Marissa: 12t
Kim: 18(t - 1/2)
YES, right on FD! You're doing rather well for a 6th grader.
And as MrsPi told you, since the distances are the same, then:
18(t - 1/2) = 12t
multiply out the left side:
18t - 9 = 12t : follow that?
Add 9 to both sides:
18t = 12t + 9 : ok?
Subtract 12t from each side:
6t = 9 : ok?
Divide each side by 6:
t = 9/6 = 3/2 = 1 1/2 : one and a half hour; ok?

So Marissa travelled 1 1/2 hours at 12 miles per hour; 12 times 1 1/2 = 18;
and Kim thavelled 1 hour (1/2 hour less) at 18 mph; 18 times 1 = 18;
so we see that distances are the same...

Don't panic if you don't fully follow that; just look at it for now...
 
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