Since the distance d is a linear function of his total driving time t, we can write:
d = at + b
with a and b constants.
Now, for d = 62, t = 16. So:
62 = a * 16 + b
Also, for d = 41.1, t = 38. So:
41.1 = a * 38 + b
Then, we can use those two equations two find the values of a and b, and then find the distance d when t = 42.
From the first equation, we obtain:
62 = a * 16 + b
62 - 16a = b
Now, we can use this expression for b into the second equation to find a:
41.1 = a * 38 + b
41.1 = 38a + 62 - 16a
41.1 = (38 - 16)a + 62
41.1 = 22a + 62
22a = 41.1 - 62
22a = -20.9
a = -20.9/22
a = -0.95
Now, we can use the value of a to find b:
b = 62 - 16a
b = 62 - 16 * (-0.95)
b = 62 + 15.2
b = 77.2
Thus, the relation between d and t is:
d = -0.95t + 77.2
Then, using t = 42, we find:
d = -0.95 * 42 + 77.2
d = -39.9 + 77.2
d = 37.3
Therefore, after 42 minutes of driving, he will have 37.3 miles to his destination.