Question

Two cars travel in the same direction along a straight highway, one at a constant speed of 53 mi/h and the other at 65 mi/h. Assuming they start at the same point. How far must the faster car travel before it has a 16 min lead on the slower car?

Answer in units of mi

Answer 1

We can use the formula distance = rate x time to solve this problem. Let d be the distance that the faster car must travel before it has a 16 min lead on the slower car. Since the faster car is traveling at a rate of 65 mi/h and the slower car is traveling at a rate of 53 mi/h, the faster car gains on the slower car at a rate of 12 mi/h (65 mi/h - 53 mi/h).

To find the time it takes for the faster car to have a 16 min lead on the slower car, we need to convert 16 min to hours by dividing by 60: 16 min / 60 = 0.267 hours.

Now we can use the formula distance = rate x time to solve for d: d = 12 mi/h x 0.267 hours = 3.204 mi. Therefore, the faster car must travel 3.204 miles before it has a 16 min lead on the slower car

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Answer 2

To determine how far the faster car must travel before it has a 16-minute lead on the slower car, we can use the formula:

Distance = Speed × Time

Let's calculate the distance traveled by each car in 16 minutes:

1. Slower car:

• Speed: 53 mi/h
• Time: 16 minutes = 16/60 hours (convert minutes to hours)
• Distance = 53 mi/h × (16/60) h = 8.9333... miles

2. Faster car:

• Speed: 65 mi/h
• Time: 16 minutes = 16/60 hours (convert minutes to hours)
• Distance = 65 mi/h × (16/60) h = 17.3333... miles

The faster car must travel approximately 17.3333... miles before it has a 16-minute lead on the slower car.

Therefore, the correct answer is: The faster car must travel approximately 17.3333... miles..^^