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1. A search plane has a cruising speed of 250 miles per hour and carries enough fuel
for at most 5 hours of flying. If there is a wind that averages 30 miles per hour and
the direction of the search is with the wind one way and against it the other,
how far can the search plane travel before it has to turn back?
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Let d be one-way distance, in miles.
Time to fly with the wind is = hours.
Time to fly against the wind is = hours.
Total time flying in both directions is + hours.
An equation for the maximum possible distance d is
+ = 5 hours.
To solve, multiply both sides by 280*220. You will get
220d + 280d = 5*280*220
Simplify and find d
500d = 308000
5d = 3080
d = 3080/5 = 616.
ANSWER. The maximum one way distance is at most 616 miles.
CHECK. + = 2.2 + 2.8 = 5 hours.
Solved.
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By the way, I found that this problem was solved at this forum several/many years ago. See the links
https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.200086.html#google_vignette
https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.646572.html#google_vignette
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Comment from student: Perfect. How about question 2? Rescue at Sea A life raft, set adrift from a sinking ship
150 miles offshore, travels directly toward a Coast Guard station at the rate of 5 miles per hour.
At the time that the raft is set adrift, a rescue helicopter is dispatched from the Coast Guard station.
If the helicopter’s average speed is 90 miles per hour, how long will it take the helicopter to reach the life raft?
Here is my set up: 5x + 90x = 150 Correct?
My response : Yes, it is correct.
You may continue from this point.
At this forum, there is a rule and a policy: One and only one problem per post.
Therefore, please do not pack more than one problem per post.