2 trains going opposite directions leave at the same time. Train b is 10mph faster than train a. in 8 hours the trains are 960 miles apart. find the speed of each
X MPH = train a speed,
(x + 10) mph = train b speed,
d1 + d2 = 960 m1,
8x + 8(x + 10) = 960,
8x + 8x + 80 = 960,
16x + 80 = 960,
16x = 960 - 80,
16x = 880,
x = 55 mph,
(x + 10) = 55 + 10 = 65 mph.
To find the speed of each train, we can set up a system of equations based on the information given.
Let's assume the speed of Train A is x mph.
Since Train B is 10 mph faster than Train A, the speed of Train B would be (x + 10) mph.
Now, we need to use the formula: Distance = Speed × Time to find the total distances covered by the two trains in 8 hours.
The distance covered by Train A in 8 hours is 8x miles.
The distance covered by Train B in 8 hours is 8(x + 10) miles.
According to the problem, the sum of the distances covered by both trains is 960 miles.
So, we can write the equation: 8x + 8(x + 10) = 960.
Simplifying the equation:
8x + 8x + 80 = 960
16x + 80 = 960
16x = 880
x = 55
The speed of Train A is 55 mph.
To find the speed of Train B, we can substitute the value of x into the expression x + 10:
55 + 10 = 65
Therefore, the speed of Train B is 65 mph.
So, Train A is traveling at 55 mph and Train B is traveling at 65 mph.