Answer:
a) 40 mph
b) 24 mph
c) 30 mph
Step-by-step explanation:
The formula to find the average speed, given the distance and the time, is:
[tex]\boxed{\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}}[/tex]
[tex]\hrulefill[/tex]
Part a)
The distance from home to town A is 20 miles.
Given that the journey takes 30 minutes, the average speed is:
[tex]\text{Speed}=\dfrac{20\; \sf miles}{30\; \sf minutes}[/tex]
Convert the time into hours:
[tex]\text{Speed}=\dfrac{20\; \sf miles}{\frac{1}{2}\; \sf hours}[/tex]
[tex]\text{Speed}=40\;\sf mph[/tex]
So, the average speed of the journey from home to town A is 40 miles per hour.
[tex]\hrulefill[/tex]
Part b)
The distance from home to town B is 20 miles.
Given that the journey takes 50 minutes, the average speed is:
[tex]\text{Speed}=\dfrac{20\; \sf miles}{50\; \sf minutes}[/tex]
Convert the time into hours:
[tex]\text{Speed}=\dfrac{20\; \sf miles}{\frac{5}{6}\; \sf hours}[/tex]
[tex]\text{Speed}=\dfrac{20\cdot 6}{5}\;\sf mph[/tex]
[tex]\text{Speed}=\dfrac{120}{5}\;\sf mph[/tex]
[tex]\text{Speed}=24\;\sf mph[/tex]
So, the average speed of the journey from home to town B is 24 mph.
[tex]\hrulefill[/tex]
Part c)
The distance from town A to home and then to town B is 40 miles.
Given that the journey takes 80 minutes, the average speed is:
[tex]\text{Speed}=\dfrac{40\; \sf miles}{80\; \sf minutes}[/tex]
Convert the time into hours:
[tex]\text{Speed}=\dfrac{40\; \sf miles}{\frac{4}{3}\; \sf hours}[/tex]
[tex]\text{Speed}=\dfrac{40\cdot 3}{4}\; \sf mph[/tex]
[tex]\text{Speed}=\dfrac{120}{4}\; \sf mph[/tex]
[tex]\text{Speed}=30\; \sf mph[/tex]
So, the average speed of the journey is 30 mph.
