Alex was biking along a 48 mile trail. first half of the time he was biking twice as fast as the second half of the time. if he spent 4 hours on the road, how fast was he biking at first?

The speed in the first part is 16 mph.

Step-by-step explanation:

The total distance is 48 miles. The total time is 4 hours.

In the second part of the trip, he was traveling at speed s for distance d for 2 hours.

In the first part of the trip he was traveling at twice the speed, or 2s, for distance 48 - d, for 2 hours.

speed = distance/time

distance = speed * time

First part of trip:

48 - d = 2s * 2

d + 4s = 48   Equation 1

Second part of the trip:

d = s * 2

d = 2s    Equation 2

Equations 1 and 2 form a system of equations in two unknowns, d and s.

d + 4s = 48

d = 2s

Substitute 2s for d in equation 1.

2s + 4s = 48

6s = 48

s = 8

The speed in the second part is 8 mph.

The speed in the first part is 2s = 2(8) = 16.

The speed in the first part is 16 mph.

Check:

d = 2s = 2(8) = 16

48 - d = 48 - 16 = 32

The second part is 16 miles. The first part is 32 miles.

16 miles at 8 mph takes 2 hours.

32 miles at 16 mph takes 2 hours.

2 hours + 2 hours = 4 hours.

Our answer is correct.

The speed in the first part is 16 mph.

The speed in the first part is 16 mph.  

Step-by-step explanation:

The total distance is 48 miles. The total time is 4 hours.  

In the second part of the trip, he was traveling at speed s for distance d for 2 hours.  

In the first part of the trip he was traveling at twice the speed, or 2s, for distance 48 - d, for 2 hours.  

speed = distance/time  

distance = speed * time  

First part of trip:  

48 - d = 2s * 2  

d + 4s = 48   Equation 1  

Second part of the trip:  

d = s * 2  

d = 2s    Equation 2  

Equations 1 and 2 form a system of equations in two unknowns, d and s.  

d + 4s = 48  

d = 2s  

Substitute 2s for d in equation 1.  

2s + 4s = 48  

6s = 48  

s = 8  

The speed in the second part is 8 mph.  

The speed in the first part is 2s = 2(8) = 16.  

The speed in the first part is 16 mph.  

Check:  

d = 2s = 2(8) = 16  

48 - d = 48 - 16 = 32  

The second part is 16 miles. The first part is 32 miles.  

16 miles at 8 mph takes 2 hours.  

32 miles at 16 mph takes 2 hours.  

2 hours + 2 hours = 4 hours.  

Our answer is correct.

The speed in the first part is 16 mph

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation:

answer: i don't understand. what are the options

step-by-step explanation: