# chart problem: At what time did the planes pass each other?

##### Junior Member
i need help on this problem. i cant figure out how to do any of it. it even stumped my parents!

At noon, a plane left Austin for Los Angeles, 2100 km away, flying at 500 km per hour. One hour later, a jet left Los Angeles for Austin at 700 km per hour. At what time did they pass each other?

Code:
|-------|------|------|----------|
|       | rate | time | distance |
|=======|======|======|==========|
| plane | 500  |   t  |          |
|-------|------|------|----------|
|  jet  | 700  |   ?  |          |
|-------|------|------|----------|
im using rt=d

#### Mrspi

##### Senior Member
Re: chart problem help

at noon a plane left austin for los angeles, 2100 km away, flying at 500 km per hour.one hour later a jet left los angeles for austin at 700 km per hour. at what time did they pass each other?
Let t = time for the plane which left from Austin

The rate for that plane is 500 km/hr. So, in t hours, the plane travels 500t km (because distance= rate * time)

The second plane left LA one hour later. So, the time traveled by the second plane is t - 1 hours.

The rate for the second plane is 700 km/hr. That plane traveled a distance of 700(t - 1) km.

Now, one plane left LA and the other plane left Austin. When they PASS each other, the distances traveled by the two planes must add up to the total distance between the two cities, or 2100 km. So,

Distance for first plane + distance for second plane = distance between LA and Ausin

500t + 700(t - 1) = 2100

Ok...solve that for t. And that will be the time traveled by the first plane; when the first plane has traveled t hours, the two planes will be passing each other.

#### Denis

##### Senior Member
Re: chart problem help

Hey sadsack, may I suggest that it may be easier if you make equations instead of these charts...?

##### Junior Member
Denis said:
Hey sadsack, may I suggest that it may be easier if you make equations instead of these charts...?
we have to use charts on these problems because that is the lesson

the answer i got is 2.33333333333.... is that right? if it is, than how do i change it into something i can use to find the time?

#### Denis

##### Senior Member
the answer i got is 2.33333333333.... is that right? if it is, than how do i change it into something i can use to find the time?
.333333 = 1/3 : what's 1/3 of 1 hour ?

##### Junior Member
oh. so they passed each other at 3:20

#### stapel

##### Super Moderator
Staff member
Re: chart problem: At what time did the planes pass each oth

Code:
|-------|------|------|----------|
|       | rate | time | distance |
|=======|======|======|==========|
| plane | 500  |   t  |          |
|-------|------|------|----------|
|  jet  | 700  |   ?  |          |
|-------|------|------|----------|
im using rt=d
If you must fill in a chart (to make your teacher happy), then use what you're given, along with the equation "d = rt".

If the first guy's time was "t" hours and the second guy took off one hour later, what is the second guy's "time" expression. Replace the "?" with this expression.

If the first guy's rate was 500 and his time was t, then, since d = rt, what is the first guy's expression for "d"? Fill in that blank. Use similar reasoning to fill in the blank for the second guy's "distance" expression.

If the total distance covered (one guy from one direction and the other guy from the other) was 2100, then what was the sum of the two "distance" expressions? Use this to create your equation. (If you have to do this on the chart, then make another row, and add down the last column to fill in a "total distance" expression.)

Eliz.