SOLUTION: Steve traveled 200 miles at a certain speeed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.
Question 164638This question is from textbook
: Steve traveled 200 miles at a certain speeed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle. This question is from textbook
You can put this solution on YOUR website! Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=the speed of Steve's vehicle
Let t=time required to travel 200 mi at this certain speed, so:
t=200/r --------------------eq1
Now we are also told that:
t-1=200/(r+10)--------------------eq2
substitute t=200/r from eq1 into eq2 and we get:
(200/r)-1=200/(r+10) multiply each term by r(r+10)
200(r+10)-r(r+10)=200r get rid of parens (distributive)
200r+2000-r^2-10r=200r subtract 200r from each side
200r-200r+2000-r^2-10r=200r-200r collect like terms
-r^2-10r+2000=0 multiplpy each term by -1
r^2+10r-2000=0--Quadratic in standard form and it can be factored
(r+50)(r-40)=0
r+50=0
r=-50-------------------disregard negative value for r; rates are positive in this problem
and
r-40=0
r=40 mph------------speed of Steve's vehicle
CK
200/40=5 hrs
200/50=4 hrs
Hope this helps---ptaylor
