Let's analyze the problem step-by-step.

Problem Summary

• Andrew and Benjamin together can paint a car in 20 hours.
• They start working together, but after 4 hours, Andrew leaves.
• Benjamin finishes the remaining work alone in 24 hours.
• We need to find how long Andrew alone would take to paint the entire car.

Step 1: Define variables

• Let Andrew's rate be AAA cars per hour.
• Let Benjamin's rate be BBB cars per hour.

From the problem:

• Together, they paint 1 car in 20 hours, so their combined rate is:

A+B=120(cars per hour)A+B=\frac{1}{20}\quad \text{(cars per hour)}A+B=201​(cars per hour)

Step 2: Work done in the first 4 hours together

In 4 hours, working together, they paint:

4×(A+B)=4×120=420=15of the car4\times (A+B)=4\times \frac{1}{20}=\frac{4}{20}=\frac{1}{5}\quad \text{of the car}4×(A+B)=4×201​=204​=51​of the car

Step 3: Remaining work

The remaining work after 4 hours is:

1−15=451-\frac{1}{5}=\frac{4}{5}1−51​=54​

Step 4: Benjamin finishes the remaining work alone in 24 hours

Benjamin's rate BBB is:

B=worktime=4524=45×24=4120=130cars per hourB=\frac{\text{work}}{\text{time}}=\frac{\frac{4}{5}}{24}=\frac{4}{5\times 24}=\frac{4}{120}=\frac{1}{30}\quad \text{cars per hour}B=timework​=2454​​=5×244​=1204​=301​cars per hour

Step 5: Find Andrew's rate

Recall:

A+B=120A+B=\frac{1}{20}A+B=201​

Substitute B=130B=\frac{1}{30}B=301​:

A+130=120A+\frac{1}{30}=\frac{1}{20}A+301​=201​

A=120−130=360−260=160A=\frac{1}{20}-\frac{1}{30}=\frac{3}{60}-\frac{2}{60}=\frac{1}{60}A=201​−301​=603​−602​=601​

Step 6: Find how long Andrew alone takes to paint the car

Andrew's rate is 160\frac{1}{60}601​ cars per hour, so time taken is:

Time=1A=60 hours\text{Time}=\frac{1}{A}=60\text{ hours}Time=A1​=60 hours

Final answer:

Andrew alone can paint the entire car in 60 hours.