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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