Answer: speed of car = 50 mph and speed of bus = 30 mph
Let the time be t
speed of car = [tex]v_c[/tex]
speed of bus = [tex]v_b[/tex]
converting the following statements in the form of equation:
car covers 300 miles in the same amount of time as bus covers 180 miles.
[tex]t=\frac{300}{v_c}=\frac{180}{v_b}[/tex] ---1
The speed of bus is 20 miles slower than the speed of the car.
[tex]v_b=v_c-20[/tex] ---2
Substitute equation 2 in 1:
[tex]\frac{300}{v_c}=\frac{180}{ v_c-20}\\ \Rightarrow 300(v_c-20)=180 v_c\\ \Rightarrow 300v_c-180v_c=6000\\ \Rightarrow v_c=\frac {6000}{120}=50 \hspace{1mm}mph[/tex]
From equation 2, we can calculate the speed of bus:
[tex]v_b=50-20=30 \hspace{1mm}mph[/tex]
Hence, the speed of car is 50 mph and speed of bus is 30 mph
