SOLUTION: Maria drove 150 miles from home to her parent's place. She drove at a constant speed. Later, she drove home 150 miles back again at a constant speed. Her drive back took .5 hours l

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Question 1102237: Maria drove 150 miles from home to her parent's place. She drove at a constant speed. Later, she drove home 150 miles back again at a constant speed. Her drive back took .5 hours longer because her speed was 10 miles per hour slower. How many hours did she drive TO her parents?
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = her speed in mi/hr going to her parents
Let +t+ = her time in hrs to go to her parents
+s+-+10+ = her speed in mi/hr driving home

Driving home:
(2) +150+=+%28+s+-+10+%29%2A%28+t+%2B+.5+%29+
-----------------------------------
(2) +150+=+s%2At+-+10t+%2B+.5s+-+5+
(2) +155+=+t%2A%28+s+-+10+%29+%2B+.5s+
and
(1) +t+=+150%2Fs+
plug this into (2)
(2) +155+=+%28+150%2Fs+%29%2A%28+s+-+10+%29+%2B+.5s+
(2) +155+=+150+-+1500%2Fs++%2B+.5s+
(2) +.5s+-+1500%2Fs+=+5+
(2) +.5s%5E2+-+1500+=+5s+
(2) +%281%2F2%29%2As%5E2+-+5s+-+1500+=+0+
(2) +s%5E2+-+10s+-+3000+=+0+
(2) +%28+s+-+60+%29%2A%28+s+%2B+50+%29+=+0+ ( by looking at it )
(2) +s+=+60+ ( can't have negative speed )
and
(1) +t+=+150%2Fs+
(1) +t+=+150%2F60+
(1) +t+=+2.5+
It took 2.5 hrs to drive to her parents house
-----------------------------------------
check:
(2) +150+=+%28+s+-+10+%29%2A%28+t+%2B+.5+%29+
(2) +150+=+%28+60+-+10+%29%2A%28+2.5+%2B+.5+%29+
(2) +150+=+50%2A3+
(2) +150+=+150+
OK
Get a 2nd opinion if needed



Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The other tutor's answer is right. She checked it, and it worked, so it was right.

I think she did a lot more work than necessary to set up the problem.

Using her same notation of s and s-10 for the two speeds, we know that the difference between the time at the lower speed and the time at the higher speed was .5 hours. So

150%2F%28s-10%29+-+150%2Fs+=+.5
300%2F%28s-10%29+-+300%2Fs+=+1
300s+-+300%28s-10%29+=+s%28s-10%29
3000+=+s%5E2-10s
s%5E2-10s-3000+=+0

... which is the equation she ended up with after doing a lot more work.

The solution from there is the same.

%28s-60%29%28s%2B50%29+=+0

The higher speed s is 60; the lower speed is 60-10=50. The time it took to drive to her parents (at the higher speed) was 150/60 = 2.5 hours.