When ABC car wash opened its doors at 9 AM, there were already 10 cars waiting in line (first come first serve). New cars arrive at the average rate of 20 cars per hour. The car wash can wash the car at the average rate of 15 cars per hour. If a new car arrives at 10 AM, how many hours should this car expect to wait before it is washed

The car that arrives at 10 AM will have to wait for at least 1 hour before it is washed.

Explanation:

First of all, let us lay out the important points:

at 9 AM; 10 cars were already waiting

arrival rate = 20 cars per hour

wash rate = 15 cars per hour.

New car arrives at 10 AM

From the statements above, if 20 cars arrive every hour, it can be inferred that between 9 AM to 10 AM, the number of new cars that arrive = 20 cars.

But remember that before the car was opened, 10 cars were already waiting in line, therefore the total number of cars that arrived between 9 AM and 10 AM = 20 + 10 = 30 cars.

We are also told that the rate of wash of the cars are; 15 cars every hour. Therefore between 9 AM and 10 AM which is 1 hour, 15 out of 30 cars were washed, leaving 15 more cars unwashed. To wash this 15 remaining cars, another hour will pass, so by 11 AM, the cars that arrived between 9 AM and 10 AM will be completely washed. hence the car that arrived at 10 AM, will wait till 11 AM in order to be washed, which is a wait time of 1 hour.

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