Petiol tank currently holds 65 litres. He travels xhours. consuming petrol at 3 litres per hour. than it decideg to quicken the sped, increasing petrol censumption at 5 litres per hour whilst driving for $$ y $$ hours there after. Determine the a igebrac experssion for the remaining lit of petrol left.

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To determine the algebraic expression for the remaining litres of petrol left in the tank, we can break down the problem step by step.

1. **Initial Conditions:**
   - The tank currently holds $$ 65 $$ litres of petrol.
   - The petrol consumption rate for the first part of the journey is $$ 3 $$ litres per hour for $$ x $$ hours.
   - After $$ x $$ hours, the consumption rate increases to $$ 5 $$ litres per hour for $$ y $$ hours.

2. **Calculating Petrol Consumption:**
   - The total petrol consumed during the first part of the journey (for $$ x $$ hours) is:
     $$
     \text{Consumption}_1 = 3x
     $$
   - The total petrol consumed during the second part of the journey (for $$ y $$ hours) is:
     $$
     \text{Consumption}_2 = 5y
     $$

3. **Total Petrol Consumed:**
   - The total petrol consumed during the entire journey is:
     $$
     \text{Total Consumption} = \text{Consumption}_1 + \text{Consumption}_2 = 3x + 5y
     $$

4. **Remaining Petrol:**
   - The remaining litres of petrol in the tank after the journey can be calculated by subtracting the total consumption from the initial amount of petrol:
     $$
     \text{Remaining Petrol} = 65 - (3x + 5y)
     $$

5. **Final Expression:**
   - Therefore, the algebraic expression for the remaining litres of petrol left in the tank is:
     $$
     R = 65 - (3x + 5y)
     $$

This expression $$ R = 65 - (3x + 5y) $$ represents the remaining litres of petrol after travelling for $$ x $$ hours at 3 litres per hour and $$ y $$ hours at 5 litres per hour.
The remaining litres of petrol left in the tank is $$ 65 - 3x - 5y $$.

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