Mark made a business trip of 290 miles. He averaged 56 mph for the first part of the trip and 60 mph for the second part. If the trip took 5 hours, how long did he travel at each rate?

time for first trip --- x hrs

time for 2nd part of trip ---- (5-x)

distance for 1st part = 56x miles
distance for 2nd part = 60(5-x)

so solve:
56x + 60(x-5) = 290

To solve this problem, we need to set up a system of equations based on the given information. Let's assume that Mark traveled for "x" hours at 56 mph and "5 - x" hours at 60 mph.

The formula to calculate distance is: distance = rate * time.

For the first part of the trip, the distance is given as 56 mph * x hours = 56x miles.

For the second part of the trip, the distance is given as 60 mph * (5 - x) hours = 60(5 - x) miles.

The total distance traveled is given as 290 miles.

Hence, we can set up the following equation based on the given information:

56x + 60(5 - x) = 290.

To solve this equation, let's distribute and simplify:

56x + 300 - 60x = 290.

Combine like terms:

-4x + 300 = 290.

Move 300 to the right side of the equation by subtracting it from both sides:

-4x = 290 - 300.

Simplify:

-4x = -10.

Now, divide both sides of the equation by -4:

x = -10 / -4 = 2.5.

So, Mark traveled for 2.5 hours at 56 mph and for (5 - 2.5) = 2.5 hours at 60 mph.

Therefore, Mark traveled at each rate for 2.5 hours.