SOLUTION: A military drone can fly at 7 miles per hour in calm conditions. For one flight, the drone flew 54 miles with the wind and 30 miles against the wind in the same amount of time. Wha

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Question 1199975: A military drone can fly at 7 miles per hour in calm conditions. For one flight, the drone flew 54 miles with the wind and 30 miles against the wind in the same amount of time. What was the wind speed for the flight? (Do not include the units in your response.)
Found 3 solutions by Alan3354, josgarithmetic, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A military drone can fly at 7 miles per hour in calm conditions. For one flight, the drone flew 54 miles with the wind and 30 miles against the wind in the same amount of time. What was the wind speed for the flight?
----------------------------
w = wind speed
===
t*(w+7) = 54
t*(w-7) = 30
---
tw + 7t = 54
tw - 7t = 30
---------------------- Add
2tw = 84
tw = 42
------
42 + 7t = 54
7t = 12
t = 12/7 hours
=====
w = 42/t = 294/12 = 24.5 mi/hr
======================================
The launch was not a good idea. The drone is miles away and can't return against the wind which is 3.5 times its airspeed.

Answer by josgarithmetic(39792) About Me  (Show Source):
You can put this solution on YOUR website!
                      SPEED             TIME           DISTANCE
WITHWIND               7+w              54/(7+w)        54
AGAINSTWD              7-w              30/(7-w)        30

The time is the same amount for both directions.
54%2F%28w%2B7%29=30%2F%28-w%2B7%29
-
9%2F%28w%2B7%29=5%2F%28-w%2B7%29
9%28-w%2B7%29=5%28w%2B7%29
-9w%2B9%2A7=5w%2B5%2A7
28=14w
highlight%28w=2%29

Answer by greenestamps(13327) About Me  (Show Source):
You can put this solution on YOUR website!


let w be the wind speed. Then the two speeds with and against the wind are 7+w and 7-w.

The ratio of the distances is 54:30 = 9:5. Since the times are the same, the ratio of speeds is also 9:5.

%287%2Bw%29%2F%287-w%29=9%2F5

The equation can be solved by inspection, although formal algebra could be used.

ANSWER: w = 2