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
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) (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.
SPEED TIME hours DIST. kilom
GOING 240 x/240 x
RETURN 320 x/320 x
TOTAL 35/60=7/12 2x
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:
Multiply by the least common denominator, 960, to clear fractions:
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.