Mary and John are 128 miles apart. A car leaves Mary traveling towards John and another car leaves John at the same time traveling towards Mary. The car leaving Mary averages 10 miles per hour more than the other car and they meet after 1 hour and 36 minutes. What are the average speeds of the cars?

since distance = speed * time,

(x + x+10)(1.6) = 128
2x+10 = 80
x = 35

So, Mary's car goes 35 mi/hr, and
John's car goes 45 mi/hr

To solve this problem, we can use the formula: Distance = Speed * Time.

Let's assume the speed of the car leaving Mary is S mph. Since the other car is traveling 10 mph slower, its speed would be (S - 10) mph.

The car leaving Mary has traveled for 1 hour and 36 minutes, which is equivalent to (1 + 36/60) hours. Let's denote this time as T hours.

Now, we can set up the equations:
Distance traveled by the car leaving Mary = Distance traveled by the other car
(S * T) = ((S - 10) * T)

It is given that the distance between Mary and John is 128 miles, so we can write:
S * T + (S - 10) * T = 128

Plugging in the value of T, we get:
S * (1 + 36/60) + (S - 10) * (1 + 36/60) = 128

Now, we can solve this equation to find the value of S, representing the speed of the car leaving Mary.