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Issue with error C2679: binary '+=': no operator found which takes a right-hand operand of type 'int'

I'm working on a piece of code for school, defining a Time class with various functions such as adding and setting time. The issue I have right now is overloading my "+=" operator.

Time& Time::operator+=(Time& a) {
    *this = a + *this;
    return *this;
}

I have overloaded the "+" operators already, so I am just calling on it for my "+=" operator.

 Time operator+(Time a, Time b) {

        int sumhr = a.hour + b.hour;
        int summin = a.minute + b.minute;

        if (summin > 59) {
            sumhr += summin / 60;
            summin = summin % 60;
        }

        if (sumhr > 23)
            sumhr = sumhr % 24;

        return Time(sumhr, summin);
    }

    Time operator+(Time a, int addminutes) {
        Time t = a + Time(addminutes);
        return t;
    }

    Time operator+(Time a, double addhours) {
        Time t = a + Time(addhours);

        return t;
    }

In my int main(), I am using:

Time c(61);
c += 120;
cout << "\tc += 120;\t\t";
cout << "c = " << c << "\n";

which gives me the error. I'm not sure what I'm doing wrong, since I overloaded the "+" operator with int and double parameters already.

What can be done to solve this problem ?

Here is the full class definition and declaration. I'm working on creating the class and running it against a driver provided by my professor, so the int main() can't be changed.

#include <iostream>

using namespace std;
using std:: cout;

class Time {
private:
    int hour;
    int minute;
public:
    Time();
    Time(int min);
    Time(int hr, int min);
    Time(double hrs);
    int minutes();
    int hours();
    Time& operator+=(Time& a);

    void set_minutes(int min);
    void set_minutes(double min);
    void set_hours(int hr);
    void set_hours(double hr);

    friend ostream& operator<<(ostream& os, const Time& t);
    friend Time operator+(Time a, Time b);
    friend Time operator+(Time a, int addminutes);
    friend Time operator+(Time a, double addhours);
    friend bool operator<(Time a, Time b);
    friend bool operator==(Time a, Time b);
    friend bool operator>=(Time a, Time b);
    friend bool operator!=(Time a, Time b);

};


Time::Time() {
    hour = 0;
    minute = 0;
}

Time::Time(int min) {
    if (min > 59) {
        hour = min / 60;
        minute = min % 60;
    }
    else {
        hour = 0;
        minute = min;
    }

}

Time::Time(int hr, int min) {
    if (min > 59) {
        hour = min / 60;
        minute = min % 60;
    }
    else {
        hour = hr;
        minute = min;
    }

    if (hour > 23)
        hour = hour % 24;
}

Time::Time(double hrs) {
    double fraction = 0;
    fraction = hrs - (int)hrs;
    minute = fraction * 60;
    hour = hrs - fraction;
    if (hour > 23)
        hour = hour % 24;
}

int Time::minutes() {
    return minute;
}

int Time::hours() {
    return hour;
}

ostream& operator<<(ostream& os, const Time& t)
{
    if (t.minute > 9)
        os << t.hour << ":" << t.minute;
    else
        os << t.hour << ":0" << t.minute;
    return os;
}

Time operator+(Time a, Time b) {

    int sumhr = a.hour + b.hour;
    int summin = a.minute + b.minute;

    if (summin > 59) {
        sumhr += summin / 60;
        summin = summin % 60;
    }

    if (sumhr > 23)
        sumhr = sumhr % 24;

    return Time(sumhr, summin);
}

Time operator+(Time a, int addminutes) {
    Time t = a + Time(addminutes);
    return t;
}

Time operator+(Time a, double addhours) {
    Time t = a + Time(addhours);

    return t;
}

Time& Time::operator+=(Time& a) {
    *this = a + *this;
    return *this;
}

bool operator<(Time a, Time b) {
    if (a.hour > b.hour)
        return false;
    else if (a.hour < b.hour)
        return true;
    else {
        if (a.minute > b.minute)
            return false;
        else if (a.minute == b.minute)
            return false;
        else
            return true;

    }
}

bool operator==(Time a, Time b) {
    if (a.hour != b.hour)
        return false;
    else {
        if (a.minute != b.minute)
            return false;
        else
            return true;
    }
}

bool operator>=(Time a, Time b) {
    if (a < b)
        return false;
    else
        return true;
}

bool operator!=(Time a, Time b) {
    if (a == b)
        return false;
    else
        return true;
}

void Time::set_minutes(int min) {
    minute = min % 60;

    if (minute == 60) {
        minute = 0;
    }
}

void Time::set_minutes(double min) {
    minute = (int)min % 60;

    double rounding = min = (int)min;

    if (rounding >= 0.5) {
        minute += 1;
        if (minute == 60) {
            minute = 0;
        }
    }

}

void Time::set_hours(int hr) {
    hour = hr % 24;
    if (hour == 24)
        hr = 0;
}

void Time::set_hours(double hr) {
    hour = (int)hr % 24;
    if (hour == 24)
        hr = 0;
}

int main() {
Time a;
    Time b(5);
    Time c(61);
    Time d(47, 59);
    Time X(5.0);
    Time Y(1.5);
    Time Z(25.1);

    cout << "Testing constructors:\n";
    cout << "\tTime a;\t\t\t";
    cout << "a = " << a << "\n";
    cout << "\tTime b(" << b.minutes() << ");\t\t";
    cout << "b = " << b << "\n";
    cout << "\tTime c(61);\t\t";
    cout << "c = " << c << "\n";
    cout << "\tTime d(47,59);\t\t";
    cout << "d = " << d << "\n";
    cout << "\tTime X(5.0);\t\t";
    cout << "X = " << X << "\n";
    cout << "\tTime Y(1.5);\t\t";
    cout << "Y = " << Y << "\n";
    cout << "\tTime Z(25.1);\t\t";
    cout << "Z = " << Z << "\n";

    cout << "Testing operator+:\n";
    cout << "\te = b + c;\t\te = " << b + c << "\n";
    cout << "\tf = d + 2;\t\tf = " << 2 + d << "\n";
    cout << "\tg = c + 2.75;\t\tg = " << 2.75 + c << "\n";

    cout << "Testing operator+=:\n";
    c += 120;
    cout << "\tc += 120;\t\t";
    cout << "c = " << c << "\n";
    c += 1.99166666;
    cout << "\tc += 1.99166666;\t";
    cout << "c = " << c << "\n";
    c += 1.99166667;
    cout << "\tc += 1.99166667;\t";
    cout << "c = " << c << "\n";

    cout << "Testing other member functions:\n";
    c.set_minutes(60);
    cout << "\tc.set_minutes(60);\t";
    cout << "c = " << c << "\n";
    c.set_minutes(123.45);
    cout << "\tc.set_minutes(123.45);\t";
    cout << "c = " << c << "\n";
    c.set_minutes(67.89);
    cout << "\tc.set_minutes(67.89);\t";
    cout << "c = " << c << "\n";
    cout << "\tc.set_hours(45);\t";
    c.set_hours(45);
    cout << "c = " << c << "\n";
    cout << "\tc.set_hours(1.9);\t";
    c.set_hours(1.9);
    cout << "c = " << c << "\n";
    cout << "\tc.set_hours(1.9999);\t";
    c.set_hours(1.9999);
    cout << "c = " << c << "\n";

    cout << "Testing comparison operators:\n";
    if (b < c)
        cout << b << " occurs earlier in the day than " << c << ", ";

    if (!(b == c))
        cout << "hence b != c.\n";

    if (c >= b)
        cout << c << " occurs later in the day than " << b << ", ";

    if (b != c)
        cout << "hence c != b.\n";

    return 0;

}

Solved this, thanks to the commentators. Instead of using a Time& parameter in my += operators, I change it to whatever type I am adding.

Time operator+(Time a, int addminutes) {
    Time t = a + Time(addminutes);
    return t;
}

Time operator+(Time a, double addhours) {
    Time t = a + Time(addhours);

    return t;
}

Time& Time::operator+=(int addMinutes) {
    *this = addMinutes + *this;
    return *this;
}


Time& Time::operator+=(double addhours) {
    *this = addhours + *this;
    return *this;
}

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