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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 total driving time was 3 hours and 30 minutes.

Explain all the steps and everything as clear as possible. I tried doing the problem and I can't get it right....

Here are the 4 possible answers...

A) 110 mi
B) 100 mi
C) 75 mi
D) 150 mi

2007-09-15 16:09:26 · 5 answers · asked by Anonymous in Science & Mathematics Mathematics

5 answers

divide the 185 miles into two parts, x and 185-x
Say the x is the part at 50
d/r=t
x/50=t(at 50)
(185-x)/55=t(at 55)
t(at 50)+t(at 55) = 3½
x/50+(185-x)/55=3½
11x+1850-10x=1925
x=1925-1850=75

Choice C

2007-09-15 16:17:45 · answer #1 · answered by chasrmck 6 · 2 0

As a quick estimate (since it is almost midnight) I would guess B (100 miles).

I say that because if she traveled 185 miles in 3.5 hours she averaged 52.8 miles per hour. Since the two speeds (50 and 55) average about 52.5 if she traveled equally at each that means to me that she spent around half the trip going at each. The number closest to half of 185 was 100 so I am guessing that one.

If I see this question again when I have more energy in the daytime I will write an actual equation and get a real answer mathematically that I will edit into this answer.

2007-09-15 16:21:03 · answer #2 · answered by Rich Z 7 · 1 0

For the distance of 50mi/h it will be represented with an (x), so the second rate, 55mi/h will be (y)

The woman drove a total or 185 mi so the first equation will be x + y = 185

to know the total distance traveled we need to get the rate for each so it will be x/50 + y/55 = 7/2. since 3hrs. and 30 mins. = 7/2

now, we simplify x/50 + y/55 = 7/2 by multiplying both sides by 550 since that's the least common multiple of 50, 55 and 2. you will get 11x + 10y = 1925

now, since your second equation is 11x + 10y = 1925 and your first equation is x + y = 185 and you need to cancel out ONE variable to get the value of the other one, you multiply your first equation by 10 to cancel out y OR by 11 to cancel out x. in this case i will cancel out y.

so (x + y = 185)10
= 10x + 10y = 1850

then subtract the first equation from the second equation
11x + 10y = 1925
- 10x + 10y = 1850
----------------------------
x = 75

then substitute the value of x in your first equation
x + y = 185
>> 75 + y = 185
>> y = 185 - 75
>> y = 110

since x represent the distance travelled in 50mi/h then the value of x is your answer, which is 75mi

2007-09-15 16:32:44 · answer #3 · answered by devilishlyangelic91 2 · 1 0

let t be the time it takes her to travel part of the trip at 50 mi/hr. We know that the total time is 3.5hrs, that means 3.5 - t is the time it takes her to cover the rest of the distance.

the first part of trip and the second par of the trip equals 185 miles

distance = speed * time

first part of the trip:
d = 50t

second part of the trip:
d = 55(3.5 - t)


50t + 55(3.5 - t) = 185
50t + 192.5 - 55t = 185
-5t = -7.5
t = 1.5hr

to find the distance plug the time in

d = 50(1.5)
d = 75 miles

the answer is C

hope this helps

2007-09-15 16:18:21 · answer #4 · answered by      7 · 1 0

I trip 39 miles to artwork, 6 days a week. formerly I moved somewhat nearer to artwork i become using sixty two miles one way. Now Ipersistent approximately 6 miles to what I used to contemplate my 0.5-way factor. A tip for every person that drives those distances.... Books on tape are great.

2017-01-02 06:25:00 · answer #5 · answered by ? 3 · 0 0

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