Some kids went on a bike ride. The ride was six hours long and the kids traveled 54 mi. For part of the ride they biked at a speed of 7 mph and for part of the ride they biked at a speed of 11 mph. For how long did they bike at the fist speed and how long for the other speed

Step-by-step explanation:

Let x represent the time that they spent biking at the first speed.

If the ride was six hours long, it means that the time they spent biking at the other speed is (6 - x) hours.

Distance = speed * time

For the first part of the ride, they biked at a speed of 7 mph. This means that the distance travelled during the first part of the ride is

7 * x = 7x

For part of the ride, they biked at a speed of 11 mph. This means that the distance travelled during the second part of the ride is

11 (6 - x)

Since the total distance that the kids traveled is 54 miles, then

11 (6 - x) + 7x = 54

66 - 11x + 7x = 54

11x - 7x = 66 - 54

4x = 12

x = 12/4 = 3

They spent 3 hours biking at the first speed.

They spent 6 - 3 = 3 hours biking at the other speed.