SOLUTION: A car traveled 1950 mi at a certain speed. If the speed had been 13 mph faster, the trip could have been made in 5 hr less time. Find the speed.

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Question 1071927: A car traveled 1950 mi at a certain speed. If the speed had been 13 mph faster, the trip could have been made in 5 hr less time. Find the speed.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
system%28r%2At=1950%2C%28r%2B13%29%28t-5%29=1950%29

rt%2B13t-5r-65=1950
rt%2B13t-5r-65=rt
13t-5r-65=0
13%281950%2Fr%29-5r-65=0
13%2A1950-5r%5E2-65r=0
-5r%5E2-65r%2B13%2A1950=0
r%5E2%2B13r-13%2A390=0
r%5E2%2B13r-5070=0
discriminant is 143%5E2.
r=%28-13%2B143%29%2F2
highlight%28r=65%29

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let r" be the actual speed, in mph.

Then the hypothetical speed is (r+13) mph.


Moving at the speed of "r" miles per hour, the car spends 1950%2Fr hours.

Traveling with the hypothetical speed, the car would spend 1950%2F%28r%2B13%29 hours.

The condition says

1950%2Fr+-+1950%2F%28r%2B13%29 = 5.


It is your "time" equation.  You must solve it for "r". 
To do it, multiply both sides by the common denominator r*(r+13). You will get

1950*(r+13) - 1950*r = 5r*(r+13),

1950%2A13 = 5r%5E2+%2B+5%2A13%2Ar,

r%5E2+%2B+13r+-+5070 = 0.

Factor it:

(r+78)*(r-65) = 0.


The only positive root is r = 65.

Answer. The speed of the car is 65 mph.