SOLUTION: Is this solvable? A car travels with uniform speed. If it would have traveled 10 km/h faster, it would reach the destination 2 hours earlier and if it would have traveled 10km/h

Question 305491: Is this solvable?
A car travels with uniform speed. If it would have traveled 10 km/h faster, it would reach the destination 2 hours earlier and if it would have traveled 10km/h slower, it would reach the destination 3 hours later. What is the distance covered by car.
Found 2 solutions by stanbon, JBarnum:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A car travels with uniform speed. If it would have traveled 10 km/h faster, it would reach the destination 2 hours earlier and if it would have traveled 10km/h slower, it would reach the destination 3 hours later. What is the distance covered by car.
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Uniform speed DATA:
rate = r mph ; time = h hours ; distance = rh miles
---------------------
Slower speed DATA:
rate = r-10 mph ; time = h+3 hrs ; distance = (r-10)(h+3) miles
----------------
Faster speed DATA:
rate = r+10 mph ; time = h-2 hrs ; distance = (r+10)(h-2) miles
------------------------
Equations:
(r-10)(h+3) = rh
(r+10)(h-2) = rh
-------
rh +3r - 10h - 30 = rh
rh -2r + 10h - 20 = rh
---------------------------
3r - 10h = 30
-2r+ 10h = 20
---------------------------
Add to get: r = 50 mph
----
Slower speed = r-10 = 40 mph
Faster speed = r+10 = 60 mph
===================================
Cheers,
Stan H.
Answer by JBarnum(2146) (Show Source): You can put this solution on YOUR website!
{{S=D/T}}}

____

subtract equations
solve for S

_____

i cant seem to find the answer unless you go into imaginary numbers

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -23 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

In the field of imaginary numbers, the square root of -23 is + or - .

The solution is

Here's your graph:

or i messed up somewhere, this sure is a hard problem. good luck
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