SOLUTION: I am struggling to set up and solve this problem: Mark made a business trip of 203.5 miles. He averaged 61mph for the first part of the trip and 57mph for the second part. If th

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Question 709523: I am struggling to set up and solve this problem:
Mark made a business trip of 203.5 miles. He averaged 61mph for the first part of the trip and 57mph for the second part. If the trip took 3.5 hours, how did he travel at each rate?

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


a business trip of d=203.5mil

averaged 61mph for the first part d%5B1%5D

and 57mph for the second part d%5B2%5D

the trip took t=3.5h

d%5B1%5D%2Bd%5B2%5D=203.5mil......eq. 1

d%5B1%5D=61mph%2At%5B1%5D for the first part d%5B1%5D

d%5B2%5D=57mph%2At%5B2%5D for the first part d%5B1%5D

t%5B1%5D%2Bt%5B2%5D=3.5+h.............eq. 2
d%5B1%5D=203.5mil-d%5B2%5D......eq. 1a
t%5B1%5D=3.5+h-t%5B2%5D.............eq. 2a

61mph%2At%5B1%5D%2B57mph%2At%5B2%5D=203.5mil...substitute t%5B1%5D
61mph%2A%283.5h-t%5B2%5D%29%2B57mph%2At%5B2%5D=203.5mil.....solve for t%5B2%5D
213.5mil%2A-61mpht%5B2%5D%29%2B57mph%2At%5B2%5D=203.5mil
%28-61mph%2B57mph%29t%5B2%5D=203.5mil-213.5mil
%28-4mph%29t%5B2%5D=-10mil
t%5B2%5D=-10mil%2F-4mph
highlight%28t%5B2%5D=2.5h%29

then t%5B1%5D=3.5+h-2.5h...=>...t%5B1%5D=hig1hlight%281h%29
go back to d%5B1%5D=61mph%2At%5B1%5D and solve for d%5B1%5D
d%5B1%5D=61mph%2At%5B1%5D
d%5B1%5D=61mph%2A1h
highlight%28d%5B1%5D=61mil%29
do same with d%5B2%5D
d%5B2%5D=57mph%2A2.5h
highlight%28d%5B2%5D=142.5mil%29