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?

Question

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

Impact of this question

1238 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-11-21T13:21:20

$V_{b o b} = 16 \frac{2}{3} \frac{m i l e s}{h o u r}$ $V_(bob)=16 2/3 (m i l e s)/(h o u r)$

$V_{p a t} = 11 \frac{2}{3} \frac{m i l e s}{h o u r}$ $V_(pat)=11 2/3 (m i l e s)/(h o u r)$

Explanation:

$T \cdot V = S$ $T*V=S$
V=velocity
T=time
S=route

$S_{p} = 70$ $S_p=70$
$S_{b} = 75$ $S_b=75$
$V_{p} = V_{b} - 5$ $V_p=V_b-5$
$T_{p} = T_{b} + 1.5$ $T_p=T_b+1.5$

$T_{p} \cdot V_{p} = S_{p}$ $T_p*V_p=S_p$
$T_{b} \cdot V_{b} = S_{b}$ $T_b*V_b=S_b$
$\Rightarrow$ $=>$
$(T_{b} + 1.5) \cdot (V_{b} - 5) = 70$ $(T_b+1.5)*(V_b-5)=70$
$T_{b} \cdot V_{b} = 75$ $T_b*V_b=75$

I want to find $V_{b}$ $V_b$ and $V_{p}$ $V_p$ :
$\Rightarrow$ $=>$
$(T_{b} + 1.5) \cdot (V_{b} - 5) = 70$ $(T_b+1.5)*(V_b-5)=70$
$T_{b} = \frac{75}{V_{b}}$ $T_b=75/V_b$

$\Rightarrow$ $=>$
$(\frac{75}{V_{b}} + 1.5) \cdot (V_{b} - 5) = 70$ $(75/V_b+1.5)*(V_b-5)=70$

Let $V_{b} = x$ $V_b=x$
$\Rightarrow (\frac{75}{x} + 1.5) \cdot (x - 5) = 70$ $=> (75/x+1.5)*(x-5)=70$
$\Rightarrow 75 - \frac{375}{x} + 1.5 x - 7.5 = 70$ $=> 75-375/x+1.5x-7.5=70$
$\Rightarrow - \frac{375}{x} + 1.5 x - 2.5 = 0$ $=> -375/x+1.5x-2.5=0$
$\Rightarrow - 375 + 1.5 x^{2} - 2.5 x = 0$ $=> -375+1.5x^2-2.5x=0$
$\Rightarrow 1.5 x^{2} - 2.5 x - 375 = 0$ $=> 1.5x^2-2.5x-375=0$
$\Rightarrow$ $=>$
$x_{1, 2} = \frac{2.5 \pm \sqrt{{(- 2.5)}^{2} - 4 \cdot (1.5) \cdot (- 375)}}{2 \cdot 1.5}$ $x_(1,2)=(2.5+-sqrt((-2.5)^2-4*(1.5)*(-375)))/(2*1.5)$
$=...=$
$x_1=50/3=16 2/3$
$x_2=-15$

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

Science

Math

Humanities

... and beyond

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

Explanation:

Related questions

Impact of this question