Distance math word problem?

Question

a woman drove part of a 185 mi trip at 50 mi/h and the rest at 55 mi/h. Find the distance she traveled at 50 mi/h if her toal driving time was 3h and 30 mins. can you show how it's done as well so i can learn =P, ty in advance.

Answer 1

divide the trip into a portion where she traveled x miles at 50 mi/hr and travled 185-x miles at 55 mi/hr

we know she traveled the total in a time of 3.5 hours

the distance traveled as a function of x is:

x/50 +(185-x)/55=3.5

x/50 +185/55 - x/55 = 3.5

solve for x and get x=75, so she travled 75 miles at 50 mi/hr (1.5 hrs) and then travled 110 miles at 55 mph (2 hours) for a total of 3.5 hours

Answer 2

let x be the total of time she drove at 50mi/h

let y be  the total of time she drove at 55mi/h

So,

50x+55y=185

         x+y= 3,5

Solve the system of equations above,

=>

x=  

  y=

Answer 3

She drove 2 hours in 55km (110) and 1 and 1/2 hours in 50 km.  

Answer 4

t = time @ 50 mph in hours

3.5 - t = time @ 55 mph in hours

50t + 55(3.5 - t) = 185

50t + 192.5 - 55t = 185

-5t = -7.5

t = 1.5

time @ 50 mph = 1.5 hours

time @ 55 mph = 2 hours

Answer 5

3.5 = [x / 50] + [(185 - x) / 55]     ----------  Mult both sides by 550 (LCD)

1925 = 11x + 10(185 - x)

1925 = 11x + 1850 - 10x

75 = x

75 miles @ 50 mph.