Answer:
Therefore Carl takes[tex]=16.07 mins[/tex]
Step-by-step explanation:
Speed : speed is the ratio of distance to time.
[tex]speed=\frac{distance}{time}[/tex]
The S.I unit of speed = m/s
The C.G.S unit of speed = cm/s
12 mph means 12 miles per hour.
Let the speed of Carl be x.
Carl is going 12mph faster than Rick.
Then the speed of Rick is = (x-12)mph
We know that,
[tex]time =\frac{distance}{speed}[/tex]
[tex]Time =\frac{5}{x-12}[/tex] h
45 minutes = [tex]\frac{45}{60}[/tex] h
According to the problem,
[tex]\frac{5}{x-12} =\frac{45}{60}[/tex]
[tex]\Rightarrow 45(x-12)=5\times60[/tex]
[tex]\Rightarrow45x-540 = 300[/tex]
[tex]\Rightarrow 45x=300+540[/tex]
[tex]\Rightarrow x=\frac{840}{45}[/tex]
We know that,
[tex]time =\frac{distance}{speed}[/tex]
Therefore Carl takes [tex]=\frac{5}{\frac{840}{45} } h[/tex] [tex]=\frac{5\times 45\times 60}{840} mins[/tex] [tex]=16.07 mins[/tex]
