SOLUTION: How do I right this word problem as a rational equation? Marty drove his fully loaded moving van to Memphis. With his van empty, Marty drove 15 mi/h faster and made the return tri

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do I right this word problem as a rational equation? Marty drove his fully loaded moving van to Memphis. With his van empty, Marty drove 15 mi/h faster and made the return tri      Log On


   

Question 1058617: How do I right this word problem as a rational equation?
Marty drove his fully loaded moving van to Memphis. With his van empty, Marty drove 15 mi/h faster and made the return trip in 1.5 hours less. Find the speed going to Memphis.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The description is constant travel rates problem, and not necessarily a rational equations problem. 
             SPEED        TIME      DISTANCE

LOADED       r             t          d

EMPTY       r+15          t-1.5       d

TOTAL


system%28rt=d%2C%28r%2B15%29%28t-1.5%29=d%29

t=d%2Fr
-
%28r%2B15%29%28%28d%2Fr%29-1.5%29=d
r%28r%2B15%29%28d%2Fr-1.5%29=d
%28r%2B15%29%28d-1.5r%29=d
rd%2B15d-1.5r%5E2-%2815%29%281.5%29r=d
rd%2B14d-1.5r%5E2-22.5r=0
-rd-14d%2B1.5r%5E2%2B22.5r=0
1.5r%5E2-rd%2B22.5r-14d=0
1.5r%5E2%2B%2822.5-d%29r-14d=0-----quadratic equation in r, but also d is still unknown variable.

r=%28d-22.5%2B-+sqrt%28%2822.5-d%29%5E2-4%2A1.5%2A%28-14d%29%29%29%2F3

r=%28d-22.5%2B-+sqrt%28%2822.5-d%29%5E2%2B84d%29%29%2F3

r=%28d-22.5%2B-+sqrt%28506.25-45d%2Bd%5E2%2B84d%29%29%2F3

highlight%28r=%28d-22.5%2B-+sqrt%28d%5E2%2B39d%2B506.25%29%29%2F3%29
The discriminant is not a perfect square, and you do not have enough information described to know the value of d.
This is all that can be done.

Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
How do I highlight%28cross%28right%29%29 write this word problem as a rational equation?
Marty drove his fully loaded moving van to Memphis. With his van empty, Marty drove 15 mi/h faster and made
the return trip in 1.5 hours less. Find the speed going to Memphis.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

You can write/represent the condition as this rational equation

D%2Fr+-+D%2F%28r%2B15%29 = 1.5,

where D is the distance "from A to B", r is the rate on the way "to Memphis".


But keep in mind that it gives you and you have only ONE equation for TWO unknowns.
So, the input info IS NOT ENOUGH to solve the problem completely and to get a quantitative solution/answer.


To demonstrate you that the solution to the equation (*) is not unique, 
I will put here THE LIST of possible solutions:

D =  45,  r = 15,     or

D = 100,  r = 25,     or

D = 175,  r = 35.

The writing by "josgarithmetic" is irrelevant, so you can better to ignore it.