Question

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

Answer 1

The kids biked at 7 mph for 3 hours and 11 mph for 3 hours.

Step-by-step explanation:

The kids traveled a total of 54 miles in a 6-hour bike ride. Let's assume they biked at the first speed, 7 mph, for a certain amount of time, and the remainder of the time they biked at the second speed, 11 mph. We can set up a system of equations to solve for the times:

1. Let t represent the time (in hours) that they biked at 7 mph.
2. Then, the remaining time (6 - t) represents the time (in hours) that they biked at 11 mph.
3. Based on the distances traveled at each speed, we can set up the equation: 7t + 11(6 - t) = 54.
4. Simplifying the equation gives us: 7t + 66 - 11t = 54.
5. Combining like terms gives us: -4t = -12.
6. Dividing both sides of the equation by -4 gives us: t = 3.

Therefore, they biked at the first speed, 7 mph, for 3 hours, and the remainder of the time, 6 - 3 = 3 hours, they biked at the second speed, 11 mph.

Answer 2

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.