Final answer:
The speed of the slower train is 35 mph, and the speed of the faster train is 45 mph, given that they meet in 3 hours and are 240 miles apart with a speed difference of 10 mph.
Step-by-step explanation:
The question involves finding the speeds of two trains traveling toward each other. The two trains are 240 miles apart and their speeds differ by 10mph. They meet in 3 hours. To solve the problem, let's denote the speed of the slower train as x mph. Therefore, the speed of the faster train would be x + 10 mph. The total distance covered by both trains when they meet will be 240 miles.
The distance covered by the slower train in 3 hours is 3x, and the distance covered by the faster train in 3 hours is 3(x + 10).
Together, these distances should sum up to 240 miles:
3x + 3(x + 10) = 240
Simplifying the equation:
3x + 3x + 30 = 240
6x + 30 = 240
6x = 210
x = 35
The slower train's speed is 35 mph and the faster train's speed is 35 + 10 = 45 mph.