Questions: a. Dr. Smith can see 10 patients in 2 hours. At this rate, how long would it take him to see 55 patients? b. On a map of the Thunderbird Country Club golf course, 1.5 inches equals 30 yards. How long is the 8th hold if the map shows 10 inches?

Solution Steps

a. To find out how long it would take Dr. Smith to see 55 patients, we first determine the rate at which he sees patients. Then, we use this rate to calculate the time required for 55 patients.

b. To find the actual length of the 8th hole, we use the scale given on the map. We convert the map measurement to the actual distance using the scale factor.

Dr. Smith can see 10 patients in 2 hours. Therefore, the rate at which he sees patients is: \[ \text{Rate} = \frac{10 \text{ patients}}{2 \text{ hours}} = 5 \text{ patients per hour} \]

To find out how long it would take Dr. Smith to see 55 patients, we use the rate calculated in Step 1: \[ \text{Time} = \frac{55 \text{ patients}}{5 \text{ patients per hour}} = 11 \text{ hours} \]

The map scale is given as 1.5 inches equals 30 yards. Therefore, the scale factor in yards per inch is: \[ \text{Scale Factor} = \frac{30 \text{ yards}}{1.5 \text{ inches}} = 20 \text{ yards per inch} \]

The map shows the 8th hole as 10 inches. Using the scale factor from Step 3, the actual length is: \[ \text{Actual Length} = 10 \text{ inches} \times 20 \text{ yards per inch} = 200 \text{ yards} \]

Final Answer