Answer:
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.
