SOLUTION: a private plane traveled from seattle to a rugged wilderness at an average of 132 mph. On the return trip, the average speed was 231 mph. If the total traveling time was 6 hours, h

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Question 1157210: a private plane traveled from seattle to a rugged wilderness at an average of 132 mph. On the return trip, the average speed was 231 mph. If the total traveling time was 6 hours, how far is Seattle from the wideness?
Found 4 solutions by josgarithmetic, josmiceli, greenestamps, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
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Both travel time sum to 6 hours.
d%2F132%2Bd%2F231=6
Solve for d.

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d%2F%2811%2A12%29%2Bd%2F%2811%2A21%29=6
d%2F%2811%2A2%2A2%2A3%29%2Bd%2F%2811%2A3%2A7%29=6
%287%2F7%29%28d%2F%2811%2A2%2A2%2A3%29%29%2B%284%2F4%29%28d%2F%2811%2A3%2A7%29%29=6
7d%2F%2811%2A4%2A3%2A7%29%2B4d%2F%2811%2A4%2A3%2A7%29=6
11d%2F%2811%2A4%2A3%2A7%29=6
d%2F%2884%29=6
d=84%2A6
highlight%28d=504%29

Answer by josmiceli(19441) About Me  (Show Source):
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Let +d+ = the distance between Seattle & the wilderness
Let +t+ = the time for the 1st trip in hrs
+d+=+132t+
+d+=+231%2A%28+6+-+t+%29+
+132t+=+231%2A%28+6+-+t+%29+
+132t+=+1386+-+231t+
+363t+=+1386+
+t+=+3.8182+
and
+d+=+132t+
+d+=+132%2A3.8182+
+d+=+504+
Seattle is 504 mi from wilderness
----------------------
check:
+d+=+231%2A%28+6+-+t+%29+
+504+=+231%2A%28+6+-+t+%29+
+504+=+231%2A%28+6+-+3.8182+%29+
+504+=+231%2A2.18182+
+504+=+503.996+
error due to rounding off
OK


Answer by greenestamps(13215) About Me  (Show Source):
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The distances are the same, and the ratio of the speeds is 132:231 = 4:7. That means the ratio of times is 7:4.

So 4/11 of the 6 hours was spent at the higher speed. The distance is then

%284%2F11%29%286%29%28231%29+=+%2824%2F11%29%28231%29+=+%2824%29%2821%29+=+504

Or of course you could calculate the distance as 7/11 of the total 6 hours at 132mph.

%287%2F11%29%286%29%28132%29+=+%2842%2F11%29%28132%29+=+%2842%29%2812%29+=+504


Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

a private plane traveled from seattle to a rugged wilderness at an average of 132 mph. On the return trip, the average speed was 231 mph. If the total traveling time was 6 hours, how far is Seattle from the wideness?
Let distance be D
Then we get the following TIME equation: matrix%281%2C3%2C+D%2F132+%2B+D%2F231%2C+%22=%22%2C+6%29
7D + 4D = 5,544 ------ Multiplying by LCD, 924
11D = 5,544
Distance, or highlight_green%28matrix%281%2C4%2C+%225%2C544%22%2F11%2C+%22=%22%2C+504%2C+miles%29%29
NOTHING else to this!!