SOLUTION: car traveled 432miles averaging a certain speed. If the car had gone 6 mph faster, the trip would have taken one hour less. find the average speed

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Question 836360: car traveled 432miles averaging a certain speed. If the car had gone 6 mph faster, the trip would have taken one hour less. find the average speed
Found 2 solutions by josmiceli, josgarithmetic:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the car's average speed
(1) +432+=+s%2At+
(2) +432+=+%28+s%2B6+%29%2A%28+t-1+%29+
--------------------------
(1) +s+=+432%2Ft+
and
(2) +432+=+s%2At+%2B+6t+-+s+-+6+
(2) +432+%2B+6+=+s%2A%28+t+-+1+%29+%2B+6t+
(2) +432+%2B+6+=+%28432%2Ft%29%2A%28+t+-+1+%29+%2B+6t+
(2) +438+=+432+-+432%2Ft+%2B+6t+
(2) +6+=+-432%2Ft+%2B+6t+
(2) +6t+=+-432+%2B+6t%5E2+
(2) +6t%5E2+-+6t+-+432+=+0+
(2) +t%5E2+-+t+-+72+=+0+
(2) +%28+t+-+9+%29%2A%28+t+%2B+8+%29+=+0+
----------------------------
Time can't be negative, so the answer is
+t+=+9+ hrs
----------------
(1) +432+=+s%2At+
(1) +432+=+s%2A9+
(1) +s+=+48+
The average speed is 48 mi/hr
check:
(2) +432+=+%28+s%2B6+%29%2A%28+t-1+%29+
(2) +432+=+%28+48%2B6+%29%2A%28+9-1+%29+
(2) +432+=+54%2A8+
(2) +432+=+432+
OK



Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
certain speed, r.
The trip is the same in both conditions, meaning the distance is the same.

r%2At=432, the car traveled.

%28r%2B6%29%28t-1%29=432, if the speed higher as specified.

The question asks in effect, to find r.
TWO EQUATIONS IN TWO UNKNOWNS.

Notice what happens when multiplying for the "if" equation:
rt%2B6t-r-6=432
You already have an equation giving that rt=432, so simplify to
0%2B6t-r-6=0
highlight_green%286t-r-6=0%29.
USE the simpler, "car traveled" equation again, this time, solved for t.
t=432%2Fr;
Substitute this into the simplified "if" equation and solve for r.

6%28432%2Fr%29-r-6=0
6%2A432-r%5E2-6r=0
highlight_green%28r%5E2%2B6r-6%2A432=0%29
-
This equation is now FOR YOU TO FINISH SOLVING. There may be too many factorizations for the 6%2A432 for the purpose of trying to factor the quadratic member, so a better choice is to just form and compute the discriminant, and then use it in forming the solution or solutions for r.