How would I solve this? What is the equation?

Question

Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle

Answer 1

Distance = Speed * Time

200 miles = Speed1 * Time1

Time1 = 200 / Speed1

200 miles = (Speed1+10) * (Time1-1)

Time1-1 = 200 / (Speed1+10)

Time1 = [200 / (Speed1 + 10)] +1

Time1 = (200 + Speed1 + 10) / (Speed1 + 10)

Time1 = (210 + Speed1) / (Speed1 + 10)

Therefore,

200 / Speed1 = (210 + Speed1) / (Speed1 + 10)

Crossmultiplying,

(200Speed1 + 2000) = 210Speed1 + Speed1^2

-Speed1^2 - 10Speed1 + 2000 = 0

Solve for Speed1, using quadratic equation

Speed 1 = 40 miles per hours

Answer 2

Not sure the exact equation but if it helps I think he was originally going 40mph and it took him 5 hours, if he had gone 10mph faster to 50mph he would have made 200 miles in 4 hours, an hour less than he actually did.  Sorry I couldn't give you the equation.

Answer 3

P(x) = Vt + Xi

therefore

200 = V*t –> V=200/t

this turned into

200 = (V+10)*(t–1)

combined

200 = ((200/t) + 10)*(t–1)

200 = 200(t–1)/t +10(t–1)

times everything by t

200t = 200t – 200 +10t^2 –10t

0 = 10t^2 – 10t – 200

0 = t^2 – t – 20

0 = (t+4)(t–5)

positive time t=5

V = 200/t = 40 mph