SOLUTION: An aircraft, used for fire spotting, flies from its base to locate a fire at an unknown distance, x km away. It travels straight to the fire and back, averaging 240 km/h for the

Algebra ->  Rate-of-work-word-problems -> SOLUTION: An aircraft, used for fire spotting, flies from its base to locate a fire at an unknown distance, x km away. It travels straight to the fire and back, averaging 240 km/h for the       Log On


   

Question 1205382: An aircraft, used for fire spotting, flies from its base to locate a fire at an unknown
distance, x km away. It travels straight to the fire and back, averaging 240 km/h for the
outward trip and 320 km/h for the return trip. If the plane was away for 35 minutes, find
the distance, x km.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Distance length x, is traveled two times.

The two time quantities sum to 35 minutes. 7%2F12hours 
              SPEED          TIME hours      DIST. kilom

GOING          240            x/240            x

RETURN         320             x/320           x

TOTAL                       35/60=7/12       2x

x%2F240%2Bx%2F320=7%2F12
.
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Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


First a standard algebraic solution, using distance equals rate times time.

The time in hours flying to the fire is x/240; the time in hours returning to its base is x/320; the total time is 35 minutes, which is 7/12 hours:

x%2F240%2Bx%2F320=7%2F12

Multiply by the least common denominator, 960, to clear fractions:

4x%2B3x=560
7x=560
x=560%2F7=80

ANSWER: 80 km

And then a completely different method....

The ratio of speeds going and returning is 240:320=3:4; since the distances are the same, the ratio of times at the two speeds is 4:3.

Dividing the total time of 35 minutes into two parts in the ratio 4:3 means the plane spent 20 minutes (1/3 of an hour) going to the fire at 240 km/h and 15 minutes (1/4 of an hour) returning to its base at 320 km/hr.

1/3 of an hour at 240 km/h is 80km; and 1/4 of an hour at 320 km/h is 80km.

ANSWER: 80 km