The Exponential Distribution · Try It 5

Suppose that on a certain stretch of highway, cars pass at an average rate of five cars per minute. Assume that the duration of time between successive cars follows the exponential distribution.

(a) On average, how many seconds elapse between two successive cars?
(b) After a car passes by, how long on average will it take for another seven cars to pass by?
(c) Find the probability that after a car passes by, the next car will pass within the next 20 seconds.
(d) Find the probability that after a car passes by, the next car will not pass for at least another 15 seconds.

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Introductory Statistics 2e · §5.3 The Exponential Distribution · Try It 5