Question 309433: I think I got the equation right to solve this word problem: You drive to California. On the way, you averaged 10 miles per hour less, and the drive took you 5 extra hours. What was your average speed on thw\e way to California?
This is the formula I used but not sure how to solve it:
1500=(R-10)(T+5)
Found 2 solutions by ankor@dixie-net.com, stanbon:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! You drive to California. On the way, you averaged 10 miles per hour less, and the drive took you 5 extra hours. What was your average speed on thw\e way to California?
:
I would do it this way:
:
Let r = speed on the way to Calif
then
(r+10) = speed on the return trip
:
Let 1500 mi = one way distance
:
Write a time equation; time = dist/speed
to Calif time - return time = 5 hrs
 -  = 5 hrs
:
multiply by r(r+10), results:
1500(r+10) - 1500r = 5r(r+10)
1500r + 15000 - 1500r = 5r^2 + 50r
:
Combine on the right
0 = 5r^2 + 50r - 15000
:
simplify, divide by 5, results
r^2 + 10r - 3000 = 0
:
Factors to
(r+60)(r-50) = 0
:
the positive solution is what we want here
r = 50 mph is the speed to Calif
:
:
Check solutions by finding the times: (return trip speed = 60 mph)
1500/50 = 30 hrs
1500/60 = 25 hrs
----------------
time dif: 5 hrs
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! You drive to California. On the way, you averaged 10 miles per hour less, and the drive took you 5 extra hours. What was your average speed on the way to California?
This is the formula I used but not sure how to solve it:
1500=(R-10)(T+5)
------------------------------
From-California DATA:
distance = 1500 miles ; rate = r mph ; time = t hrs
Note: rt = 1500
t = 1500/r
--------------------------
To-California DATA:
distance = 1500 miles ; rate = r-10 mph ; time = t+5 hrs
--------------------------
Note: (r-10)(t+5) = 1500
----------------------------------
You have two equations; solve the system:
rt-10t+5r-50 = 1500
1500 -10(1500/r)+5r-50 = 1500
-10(1500/r)+5r-50 = 0
Multiply thru by r to get:
-10(1500) + 5r^2 - 50r = 0
Divide thru by 5 to get:
-2(1500) + r^2 - 10r = 0
r^2 -10r - 3000 = 0
-------------------------
r = [10 +- sqrt(100+4*3000)]/2
---
r = [10 +- sqrt(12100)]/2
Positive solution:
r = [120]/2
r = 60 mph
t = 1500/60 = 25 hrs.
----------------------------------
Cheers,
Stan H.
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