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Chapter 2: Problem 43

You allow 40 min to drive 25 mi to the airport, but you're caught in heavy traffic and average only \(20 \mathrm{mi} / \mathrm{h}\) for the first 15 min. What must your average speed be on the rest of the trip if you're to make your flight?

Short Answer

Expert verified
The average speed for the rest of the trip should be approximately \(47.6 \text{ mi/hr}\).

Step by step solution

01

Convert all time measurements to the same unit

First, convert all time measurements to the same unit to simplify calculations. Here, convert 40 minutes into hours because speed is given in miles per hour. \(40 \text{ min} = \frac{40}{60}= 0.67 \text{ hours}\)
02

Calculate the distance covered in the first 15 minutes

Next, determine the distance covered in the first 15 min when the speed is \(20 \text{ mi/hr}\). The formula distance = speed * time, therefore, \(\text{Distance} = 20 * \frac{15}{60} = 5 \text{ miles}\)
03

Determine the remaining distance and time

Subtract the distance covered in the first 15 minutes from the total distance to find the remaining distance. So, \(\text{Remaining distance} = 25 - 5 = 20 \text{ miles}\). Also, subtract 15 minutes from total time, \(\text{Remaining time} = 0.67 - \frac{15}{60} = 0.42 \text{ hours}\)
04

Find the required speed

Finally, to find the average speed required for the rest of the trip, use the formula speed = distance/time. \(\text{Required speed} = \frac{20}{0.42} \approx 47.6 \text{ mi/hr}\)

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Most popular questions from this chapter

Starting from rest, a car accelerates at a constant rate, reaching \(88 \mathrm{km} / \mathrm{h}\) in 12 s. Find (a) its acceleration and (b) how far it goes in this time.

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