cout << "Please enter your destination travel start time (HH:MM): " << endl;
cin >>dest_startHOUR>>dest_startMIN;

cout << "Please enter your destination travel end time (HH:MM): " << endl;
cin >>dest_endHOUR>>dest_endMIN;

cout << "Please enter your home travel start time (HH:MM): " << endl;
cin >>home_startHOUR>>home_startMIN;

cout << "Please enter your home travel end time (HH:MM): " << endl << endl;
cin >>home_endHOUR>>home_endMIN;
cout << "Departed from " << home_city << " at " << dest_startHOUR << ":" << dest_startMIN << "." << endl;
cout << "Traveled " << dest_miles << " miles to " << dest_city << ", arrived at " <<     dest_endHOUR << ":" << dest_endMIN << ". " << "Travel time, " << dest_endHOUR - home_startHOUR << "." << (dest_endMIN - home_startMIN) / 60 << " hours."<< endl << endl;

Please enter your destination travel start time (HH:MM):
04:30
Please enter your destination travel end time (HH:MM):
Please enter your home travel start time (HH:MM):
Please enter your home travel end time (HH:MM):
Departed from CityA at 4:0.
Traveled 200 miles to CityB, arrived at 0:0. Travel time, 0.0 hours.

Please enter your destination travel start time (HH:MM): 05:30
Please enter your destination travel end time (HH:MM): 07:45
Please enter your home travel start time (HH:MM): 06:15
Please enter your home travel end time (HH:MM): 08:30

Departed from CityA at 05:30.
Traveled 100 miles to CityB, arrived at
07:45. Travel time, 2.25 hours.

#include <iostream>
#include <string>
#include <iomanip>
#include <string>

using namespace std;

...

int dest_startHOUR, dest_startMIN;
int dest_endHOUR, dest_endMIN;
int home_startHOUR, home_startMIN;
int home_endHOUR, home_endMIN;
int dest_miles;
string home_city, dest_city;
char c;

...

cout << "Please enter your destination travel start time (HH:MM): ";
cin >> dest_startHOUR >> c >> dest_startMIN;
cin.clear();
cin.ignore(numeric_limits<streamsize>::max(), 'n');

cout << "Please enter your destination travel end time (HH:MM): ";
cin >> dest_endHOUR >> c >> dest_endMIN;
cin.clear();
cin.ignore(numeric_limits<streamsize>::max(), 'n');

cout << "Please enter your home travel start time (HH:MM): ";
cin >> home_startHOUR >> c >> home_startMIN;
cin.clear();
cin.ignore(numeric_limits<streamsize>::max(), 'n');

cout << "Please enter your home travel end time (HH:MM): ";
cin >> home_endHOUR >> c >> home_endMIN;
cin.clear();
cin.ignore(numeric_limits<streamsize>::max(), 'n');

cout << endl;
cout << "Departed from " << home_city << " at " << setw(2) << setfill('0') << dest_startHOUR << ":" << dest_startMIN << "." << endl;
cout << "Traveled " << dest_miles << " miles to " << dest_city << ", arrived at " << setw(2) << setfill('0') << dest_endHOUR << ":" << dest_endMIN << ". " << endl;
cout << "Travel time, " << dest_endHOUR - home_startHOUR << "." << (dest_endMIN - home_startMIN) / 60 << " hours." << endl;
cout << endl;

#include <iostream>
#include <string>
using namespace std;

int main()
{
    int dest_startHOUR, dest_startMIN;
    int dest_endHOUR, dest_endMIN;
    int home_startHOUR, home_startMIN;
    int home_endHOUR, home_endMIN;
    int dest_miles = 200;
    string home_city = "CityA", dest_city = "CityB";
    char ch;

    cout << "Please enter your destination travel start time (HH:MM): ";
    cin >> dest_startHOUR >> ch >> dest_startMIN;

    cout << "Please enter your destination travel end time (HH:MM): ";
    cin >> dest_endHOUR >> ch >> dest_endMIN;

    cout << "Please enter your home travel start time (HH:MM): ";
    cin >> home_startHOUR >> ch >> home_startMIN;

    cout << "Please enter your home travel end time (HH:MM): ";
    cin >> home_endHOUR >> ch >> home_endMIN;

    cout << "Departed from " << home_city << " at " << dest_startHOUR << ":" << dest_startMIN << "." << endl;
    cout << "Traveled " << dest_miles << " miles to " << dest_city
        << ", arrived at " << dest_endHOUR << ":" << dest_endMIN << ". "
        << "Travel time, " << dest_endHOUR - dest_startHOUR << "." << (dest_endMIN - dest_startMIN) / 60.0 * 100
        << " hours." << endl << endl;

    return 0;
}

Please enter your destination travel start time (HH:MM): 05:30
Please enter your destination travel end time (HH:MM): 07:45
Please enter your home travel start time (HH:MM): 06:15
Please enter your home travel end time (HH:MM): 08:30
Departed from CityA at 5:30.
Traveled 200 miles to CityB, arrived at 7:45. Travel time, 2.25 hours.