What equation would I use to solve this problem?

Question

I figured out the answer for this question through guess and check, but I cannot figure out the equation I need to use to solve the problem.

Bob drove from TownA to TownB, a distance of 250 miles. He increased his speed by 10mi/hr for the 360 mile trip from TownB to TownC. If the total trip took 11 hours, what was his speed from TownA to Town B?

The answer is 50mph, but I cannot figure out how to get this without guess and check. Any help is great. Thanks.

Answer 1

x= rate from A to B
250/x = time from A to B
x+10 = rate from B to C
360/(x+10)=time from A to B

250/x+360/(x+10)=11
250(x+10)+360x=11(x+10)x
250x+2500+360x=11x²+110x
0=11x²-500x-2500
0=(11x+50 )(x-50)
x=-50/11, x=50
discard the negative value
x=50

Answer 2

Let his speed from town A to town B = x mi/hr
So, his speed from town B to town C = x + 10 mi/hr

Total time taken by him = 250/x + 360/(x + 10) = 11
=> 250(x + 10) + 360x = 11x(x + 10)
=> 11x^2 - 500x -2500 = 0
=> x = (1/22) [500 + √[(500)^2 + 44*2500]
=> x = (1/22) [ 500 + 600 ]
=> x = 50 mi/hr

Answer 3

A to B
250 miles at x miles/hr
Time taken = 250/x hrs

B to C
360 miles at (x+10) miles / hr
Time taken = 360/(x+10)

Total time = [250/x] +[360/(x+10)] = 11

This equation when solved gives x = 50, -50/11

Speed has to be positive value, so x = 50

Answer 4

well we know that v = d/t (speed = distance over time)
this means that t = d/v

so say that his initial speed is x

then time for first trip = 250/x
time for second trip = 360/(x + 10)
total time = 11

soooooo

11 = 250/x + 360/(x+10)
11x(x+10) = 250(x+10) + 360x
11x^2 + 110x = 610x + 250
11x^2 - 500x - 250 = 0
x = 50 or -50/11

obviously its 50

Answer 5

The equation for solving this problem is: Let R = Ralph's age. Then R + 6 = 2(R/3 + 6)

Answer 6

______________A to B______B to C
Speed(mph)--------x---------------x + 10
time (h)--------------t1---------------t2
distance(miles)-----250-----------360

t = t1 + t2
t = 250 / x + 360 / (x + 10)
t = [ 250(x + 10) + 360 x ] / [(x) (x + 10) ]
t = [ 610 x + 2500 ] / [ x (x + 10) ] = 11
610 x + 2500 = 11x ² + 110 x
11x² - 500x - 2500 = 0
(11x + 50) (x - 50) = 0
x = 50 mph is taken as acceptable answer.