Answer:
63 mph and 53 mph
Explanation:
We can represent the situation as:
Therefore, if we call x the speed of the train that travels east, (x-10) is the speed of the train that travels west.
Then, after 1.5 hours, they are at a distance of 171 miles and they are getting apart at a speed equal to the sum of both speeds, so we can write the following equation:
[tex]\begin{gathered} \text{speed = }\frac{dis\tan ce}{time} \\ x+(x-10)=\frac{171}{1.5} \end{gathered}[/tex]So, solving for x, we get:
[tex]\begin{gathered} x+x-10=114 \\ 2x-10=114 \\ 2x-10+10=114+10 \\ 2x=124 \\ \frac{2x}{2}=\frac{124}{2} \\ x=62 \end{gathered}[/tex]Therefore, the speed of the first train was 63 mph and the speed of the second train was 10 mph slower, so it was 53 mph.
