Pat travels 70 miles on her milk route, and Bob travels 75 miles on his route. Pat travels 5 miles per hour slower than Bob, and her route takes her one half hour longer than Bob's. How fast is each one traveling?

1 Answer
Tamir E.
Nov 21, 2017

#V_(bob)=16 2/3 (m i l e s)/(h o u r)#

#V_(pat)=11 2/3 (m i l e s)/(h o u r)#

Explanation:

#T*V=S#
V=velocity
T=time
S=route

#S_p=70#
#S_b=75#
#V_p=V_b-5#
#T_p=T_b+1.5#

#T_p*V_p=S_p#
#T_b*V_b=S_b#
#=>#
#(T_b+1.5)*(V_b-5)=70#
#T_b*V_b=75#

I want to find #V_b# and #V_p#:
#=>#
#(T_b+1.5)*(V_b-5)=70#
#T_b=75/V_b#

#=>#
#(75/V_b+1.5)*(V_b-5)=70#

Let #V_b=x#
#=> (75/x+1.5)*(x-5)=70#
#=> 75-375/x+1.5x-7.5=70#
#=> -375/x+1.5x-2.5=0#
#=> -375+1.5x^2-2.5x=0#
#=> 1.5x^2-2.5x-375=0#
#=>#
#x_(1,2)=(2.5+-sqrt((-2.5)^2-4*(1.5)*(-375)))/(2*1.5)#
#=...=#
#x_1=50/3=16 2/3#
#x_2=-15#

Velocity cannot be negative, so:
#=>#
#x=16 2/3=V_b#
#=>#
#V_p=V_b-5=16 2/3-5=11 2/3#

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