Graham is hiking at an altitude of 14,040 feet and is descending 50 feet each minute. Max is hiking at an altitude of 12,500 feet and is ascending 20 feet each minute. How many minutes will it take Graham and Max to meet at the same altitude?
a. Equation:__________________
b. Solution:__________________
c. At what altitude will Graham and Max meet?______________
Answers
Solution :-
Graham :-
- Altitude = 14,040 feet = First term.
- Descending = 50 feet = common difference .
14040 , 13990, 13940, __________ = form an AP.
Max :-
- Altitude = 12,500 feet = First term.
- Ascending = 200 feet = common difference .
12500 , 12520, 12540, __________ = form an AP .
Let us Assume that , after n minutes Graham and max meet at the same altitude .
Than,
→ in n minutes Graham will be at an altitude of = a + (n - 1)d = 14040 + (n - 1)(-50) { Descending .}
→ in n minutes Max will be at an altitude of = a + (n - 1)d = 12500 + (n - 1)20
a)
→ 14040 + (n - 1)(-50) = 12500 + (n - 1)20
b)
→ 14040 - 50n + 50 = 12500 + 20n - 20
→ 14090 - 50n = 12480 + 20n
→ 20n + 50n = 14090 - 12480
→ 70n = 1610
→ n = 23 minutes. (Ans.)
c)
→ Altitude where graham and max meet = 12500 + (n - 1)20 = 12500 + (23 - 1)20 = 12500 + 22*20 = 12500 + 440 = 12940 feet . (Ans.)
Hence, graham and max meet will be at same altitude of 12,940 after 23 minutes.
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