Answer:
It will take 36 min for the cars to be 25 miles apart
Step-by-step explanation:
Hi there!
The position of the cars after a time "t" is calculated as follows:
x = x0 + v · t
Where:
x = position of the car at time t.
x0 = initial position.
v = velocity.
t = time.
Let´s consider the origin of the system of reference as the point at which the Honda is located initially. Let´s also consider the west direction as positive:
The position of the Honda at time t will be:
x = x0 + v · t
x = 0 + 20 mi/h · t = 20 mi/h · t
The position of the other car is calculated as follows:
x = 5 mi - 30 mi/h · t
(Notice that the velocity is negative because the car travels eastwards)
When the cars are 25 miles apart, the difference between their positions is 25 miles:
position of the Honda - position of the other car = 25 mi
(notice that for the difference to be positive, the position of the Honda (which is positive because it travels westbound) has to be first in the equation)
20 mi/h · t - (5 mi - 30 mi/h · t) = 25 mi
Solving for t
20 mi/h · t - 5 mi + 30 mi/h · t = 25 mi
50 mi/h · t = 30 mi
t = 30 mi / 50 mi/h
t = 0.6 h (60 min/1 h) = 36 min
It will take 36 min for the cars to be 25 miles apart.