SOLUTION: I am sorry for asking so many math problems, but I was wondering if someone could please help me? I would deeply appreciate it!! Please and Thank You!! Rate-Time-Distance Prob

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Question 134622This question is from textbook Algebra Structure and Method
: I am sorry for asking so many math problems, but I was wondering if someone could please help me? I would deeply appreciate it!! Please and Thank You!!
Rate-Time-Distance Problems
solve.
An ultralight plane had been flying for 40 minutes when a change of wind direction doubled its ground speed. The entire trip of 160 miles took 2 hours. How far did the plane travel during the first 40 minutes?
I deeply appreciate all the help that the tutors have given me!!
This question is from textbook Algebra Structure and Method

Found 2 solutions by vleith, josmiceli:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Let s be the speed during the first 40 minutes, then 2s is the speed for the last 80 minutes.
Distance+=+w%2A%2840%2F60%29+%2B+2w%2A%2880%2F60%29
160+=+2w%2F3+%2B+8w%2F3
480+=+2w+%2B+8w
480+=+10w
48+=+w
How far did the plane go in the first 40 minutes?
Distance = rate*time = 48 * 2/3 = 32 miles.
The plane went 96*4/3 after the wind changed = 128 miles
For a total of 32+128 = 160 miles.
That wind really helped:)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Divide the trip into 2 parts:
The 1st 40 min or 2/3 hr
The next 80 min or 4/3 hr
Call the distance covered on the 1st part d
The distance covered on the 2nd part is 160+-+d
Call the ground speed on the 1st part s
The ground speed on the 2nd part is 2s
d+=+s%2A%282%2F3%29
160+-+d+=+2s%2A%284%2F3%29
Substitute d in the 1st for d in the 2nd
160+-+s%2A%282%2F3%29+=+2s%2A%284%2F3%29
multiply both sides by 3
480+-+2s+=+8s
10s+=+480
s+=+48mi/hr
d+=+48%2A%282%2F3%29
d+=+32mi
The plane travelled 32 mi during the 1st 40 min
check:
160+-+d+=+2s%2A%284%2F3%29
160+-+32+=+2%2A48%2A%284%2F3%29
128+=+128
OK