To solve the problem of finding the speed of Train A, let's break it down step by step:
1. Understanding the Problem:
- Train B travels 15 mph faster than Train A.
- The total distance covered by both trains together in 8 hours is 1000 miles.
2. Introduce Variables:
- Let the speed of Train A be denoted as [tex]\( a \)[/tex] mph.
- Consequently, the speed of Train B, which is 15 mph faster than Train A, would be [tex]\( a + 15 \)[/tex] mph.
3. Distance Formula:
- Distance covered by Train A in 8 hours is given by [tex]\( 8a \)[/tex] (because distance = speed × time).
- Distance covered by Train B in 8 hours is given by [tex]\( 8(a + 15) \)[/tex].
4. Set Up the Equation:
- The total distance covered by both trains is the sum of the distances they travel individually. According to the problem, this total distance is 1000 miles.
- So, we can write the equation:
[tex]\[
8a + 8(a + 15) = 1000
\][/tex]
5. Solve for [tex]\( a \)[/tex]:
- Expand the equation:
[tex]\[
8a + 8a + 120 = 1000
\][/tex]
- Combine like terms:
[tex]\[
16a + 120 = 1000
\][/tex]
- Subtract 120 from both sides to isolate terms involving [tex]\( a \)[/tex]:
[tex]\[
16a = 880
\][/tex]
- Divide by 16 to solve for [tex]\( a \)[/tex]:
[tex]\[
a = \frac{880}{16}
\][/tex]
[tex]\[
a = 55
\][/tex]
Therefore, the speed of Train A is 55 mph.
