Question

if a car travels 30 mi. north for 30 min., 60 mi. east for 1.0 hour, and 30 mi. south for 30 min., what is the average speed of the car over the first two legs of the trip?
○ 53.3 mph
○ 60 mph
○ 50. mph
○ 53 mph

Explanation:

Step1: Convert time to hours

First leg: 30 min = $\frac{30}{60}$ h = 0.5 h. Second leg: 1.0 h. Total time for first two legs: $0.5 + 1.0 = 1.5$ h.

Step2: Calculate total distance

First leg distance: 30 mi. Second leg distance: 60 mi. Total distance: $30 + 60 = 90$ mi.

Step3: Calculate average speed

Average speed formula: $v = \frac{d}{t}$, where $d$ is total distance, $t$ is total time. So $v = \frac{90}{1.5} = 60$ mph? Wait, no, wait: Wait, 30 mi in 0.5 h, 60 mi in 1 h. Total distance: 30 + 60 = 90 mi. Total time: 0.5 + 1 = 1.5 h. Then average speed is 90 / 1.5 = 60? Wait, but let's check again. Wait, 30 miles in 30 minutes (0.5 hours) is 60 mph, 60 miles in 1 hour is 60 mph. Wait, but average speed is total distance over total time. So (30 + 60) miles / (0.5 + 1) hours = 90 / 1.5 = 60 mph. Wait, but the options have 50? Wait, maybe I made a mistake. Wait, no: 30 minutes is 0.5 hours. So first leg: 30 mi / 0.5 h = 60 mph. Second leg: 60 mi / 1 h = 60 mph. But average speed is total distance divided by total time. So total distance: 30 + 60 = 90 mi. Total time: 0.5 + 1 = 1.5 h. 90 / 1.5 = 60 mph. So the answer should be 60 mph. Wait, but let's check the options. The options are 53.3, 60, 50, 53. So 60 is an option. Wait, maybe I miscalculated. Wait, 30 minutes is 0.5 hours. So first leg: 30 mi in 0.5 h, second leg: 60 mi in 1 h. Total distance: 30 + 60 = 90 mi. Total time: 0.5 + 1 = 1.5 h. 90 divided by 1.5 is 60. So the average speed is 60 mph.

Answer:

60 mph (corresponding to the option "60 mph")