let his original speed be x mph
then his original time is 200/x hours
let his second speed be x+10 mph
then his second time is 200/(x+10) hours
so 200/x - 200/(x+10) = 1
multiply both sides by x(x+10)
200x + 2000 - 200x = x^2 + 10x
x^2 + 10x - 2000 = 0
(x-40)(x+50) = 0
x = 40 or x= -50 (negative speed makes no sense)
so Pete's speed is 40 mph.
check: at 40 mph, it would take him 200/40 = 5 hours
at 50 mph it would have taken him 200/50 = 4 hours.
Lat V be the slower speed and T be the time it takes to go 200 miles at that speed. You can write these two equations:
T = 200/V
T = 200/(V + 10) + 1
Now get rid of the T and create and solve an equation for v alone.
200 [1/V - 1/(V+10) = 1
200(V + 10 - V) = V(V+10)
V^2 + 10V -2000 = 0
(V-40)(V+50) = 0
V = 40 since only positive roots are allowed.
Answer this Question
algebra d=rt word problem - A car travels from one town to another at a speed of...
Algebra - A car travels from one town to another at a speed of 42 mph. If it had...
Math - Pete and jan compete as a team in a biathlon. Pete runs at a speed of 9 ...
MATH Algebra - The speed of a passenger train is 6 mph faster than the speed of ...
algebra - These are very easy to set up with a "chart" ---------Distance-----...
algebra - Can someoe please help me figure this out? During the first part of a ...
intermediate algebra - The danville Express travels 280 miles at a certain speed...
algebra - during the first trip a canoeist travels 79 miles at a certain speed. ...
Algebra - During the first part of a trip, a canoeist travels 57 miles at a ...
math - Suppose that a certain municipality uses the equation y=3(x-50)+30 to ...