Linda went east at 20mph; 3 hrs later, Shana went west at...

[Sarah2391]

Can someone explain how you set up this exercise?

Linda headed east at 20mph on her bicycle at 9am. 3 hours later Shana headed west from the same place walking at 6mph. What time was
it when they were 164 miles apart?

 

[stapel]

Linda headed east at 20mph on her bicycle at 9am. 3 hours later Shana headed west from the same place walking at 6mph. What time was it when they were 164 miles apart?

Are you familiar at all with the "d = rt" equation? :?:

Thank you!

Eliz.

 

[nycfunction]

Can someone explain how you set up this exercise?

Linda headed east at 20mph on her bicycle at 9am. 3 hours later Shana headed west from the same place walking at 6mph. What time was
it when they were 164 miles apart?

We can use the distance formula, which is

d = rt, where d is the distance, r is the speed (also called rate) and t is time in terms of hours NOT minutes.

Here is what we have:

1-You know both speeds.

2-The time when they will be 164 miles apart is what we need to find.

3-The total distance given is 164 miles.

4-We also know that Linda is 3 hours ahead of Shana.

We create a table for d = rt.

....................Time..........Rate..........Distance
Linda............x + 3..........20mph.......20(x + 3)

Shana.............x.............6mph..........6x

So, we add 20(x + 3) + 6x and equated to the total miles given which is 164 miles.

In other words, we have this equation:

20(x + 3) + 6x = 164

Solve for x.

20x + 60 + 6x = 164

26x + 60 = 164

26x = 164 - 60

26x = 104

x = 104 divided by 26

x = 4

Now, the question is, at what time will they be 164 miles apart?

Linda left at 9am. For Linda's time we have x + 3, which becomes 4 + 3 = 7

9am + 7 hours = 4pm

Shana left 3 hours after Linda.

If Linda left at 9am, then Shana left at 12 noon.

Are you with me so far?

For Shana's time, we have x, which we found to equal 4.

Then 12 noon + 4 hours = 4pm

Both girls were 164 miles apart at 4pm.

Is this clear?

 

[skeeter]

alternatively, since linda got a 3 hr head start, they are 60 miles apart at noon.

now you just have to figure when they are 104 miles farther apart ...

20t + 6t = 104

solve for t and add it to the noon hour to get the time desired.

(credit to royhaas for this technique).