Ok before you tell me that I am a slacker I am in the 8th grade in honors (Algebra 1 instead of pre-algebra) math and I have been working on this for 3 hours, but I cant figure them out. Please can you give me the answers and how you got them so next time I know what to do. Thank you ahead of time!
16. A plane left Charlotte flying at an average rate of 270 mph. Two hours later, another plane left Charlotte flying at an average rate of 450mph. How long will the second plane be flying until it catches up with the first?
17. In question #16, how far did the second plane travel?
23.Find three consecutive odd integers such that the sum of seven times the smallest and twice the largest is -127.
In case you were wondering there was a total of 25 questions. Thanks once again!!!
Answers & Comments
Verified answer
the planes travel further the faster they fly and the longer they fly:
x1=v1*t1
x2=v2*t2
v1=270mph
v2=450mph
since first plane left sooner, it was flying 2h longer than second plane:
t1=2+t1
when they meet, both planes have covered same distance
x1=x2
which means
v1*t1=v2*t2
or
v1*(2+t2)=v2*t2
solve for t2 to get time second plane was flying
270*(2+t2)=450*t2
540+270t2=450t2
540=(450-270)t2
540=180t2
t2=540/180 = 3h
x2=v2*t2=450mph * 3h = 1350miles
let's pick three numbers A, B, C
they are odd integers
we need to solve
7*A+2*C=-127
we do know that B=A+2 since even and odd numbers alternate and B>A.
the same goes for C which is bigger than B so
C=B+2=A+4
7*A+2*C=-127
7*A+2*(A+4)=-127
7A+2A+8=-127
9A=-127-8
A=-135/9
A=-15
B=A+2=-13
C=B+2=-11
Number 16.
D = R x T
Plane A 270x 270 we'll call this "x"
Plane B 450(x+2) 450 x + 2 since this plane left 2 hours later
therefore,
450(x+2) = 270x
x would equal 5 hours if you now do the equation...
17. How far does the plane travel??
450mph is the speed
therefore, 450 miles per 5 hours = 450 x 5 = 2250 miles traveled
23.
Smallest Integer = x
Middle Integer = x + 2 since it is consecutive odd integer
Largest Integer = x + 4 since it is consecutive odd integer
7x + 2(x + 4) = 127
7x + 2x + 8 = 127 Smallest is 13.2, middle is 15.2, largest is 17.2
9x = 119
x = 13.2