It takes 1 hour longer to fly to St. Paul at 200mi/h than it does to return at 250 mi/h. How far away is St. Paul?
Make a DRT-chart:
DISTANCE RATE TIME
Going
Returning
------------------------------------
Let the time required to return be t.
So fill in t for the "Returning time".
DISTANCE RATE TIME
Going
Returning t
------------------------------------
We read:
>>...1 hour longer to fly to St. Paul...<<
So we fill in the "Going time" box with t+1:
DISTANCE RATE TIME
Going t+1
Returning t
------------------------------------
We read:
>>...fly to St. Paul at 200mi/h...<<
So we fill 200 in the "Going rate" box
in the chart:
DISTANCE RATE TIME
Going 200 t+1
Returning t
------------------------------------
We read:
>>...to return at 250 mi/h...<<
So we fill 250 in the "Returning rate"
box in the chart:
DISTANCE RATE TIME
Going 200 t+1
Returning 250 t
------------------------------------
Now we use the formula
DISTANCE = RATE × TIME
to fill in the "Distance Going" and the
"Distance Returning" boxes.
DISTANCE RATE TIME
Going 200(t+1) 200 t+1
Returning 250t 250 t
------------------------------------
Now we form the equation by realizing that
the "Distance Going" equals the "Distance
Returning". So we set what's in the "Distance
Going" box in the chart above, namely 200(t+1),
equal to what's in the "DISTANCE returning" box,
just below it, namely, 250t:
200(t+1) = 250t
Then we solve that equation and get t=4
But the question is:
>>...How far away is St. Paul?...<<
It doesn't ask for the time. It asks
for the distance. So we have to substitute
t=4 into either the expression for the
"distance Going" or the "distance Returning".
Substituting t=4 into the expression
for the "distance Returning":
250t
250(4)
1000
So the "distance Returning" is 1000
miles. That's the answer.
As a check, we substitute t=4 into
the expression for the "distance Going":
200(t+1)
200(4+1)
200(5)
1000
So the distance Going is 1000
miles also. So that checks, since the
distance going should be the same as
the distance returning.
Edwin