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.

Answer: The speed in the first part is 16 mph.