Answer: 96 hours
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Step-by-step explanation:
Let;
Molly = M
Peyton = P
Kurt = K
M spent twice as many hours as Peyton (M=2P). She (Peyton) spent 46 hours fewer than Kurt. (P=K-46). The total for all three balloonists was 246 hours (M+P+K=246 hours). How long did Kurt spend in the balloon? (K=?)
M=2P
P=K-46
K=?
M+P+K=246
[tex]2P+P+K=246\\[/tex]
So, now we replace P for our value above.
[tex]2(K-46)+K-46+K=246[/tex]
Distribute 2.
[tex]2K-92+K-46+K=246\\[/tex]
Solve;
[tex]2K+K+K-92-46=246\\4K-138=246[/tex]
Add 138 on both sides to isolate 4K.
[tex]+138+4K-138=246+138\\4K=384[/tex]
Divide by 4 to isolate K.
[tex]\frac{4K}{4}=\frac{384}{4}[/tex]
[tex]K=96[/tex]
Therefore, Kurt was 96 hours in the balloon.
