An electric scooter travels at a constant speed of 15 miles per hour. Given that 1\text{ m… — SAT

An electric scooter travels at a constant speed of $15$ miles per hour. Given that $1\text{ mile} = 1.6$ kilometers, how many seconds does it take the scooter to travel $100$ meters?

Answer: 15 seconds

Answer

The correct answer is 15. The scooter takes 15 seconds to travel 100 meters.

To find the time in seconds to travel 100 meters, we first convert the speed of 15 miles per hour to kilometers per hour by multiplying by 1.6, yielding 24 kilometers per hour. We then convert this speed to meters per second by multiplying by 1,000 (to convert kilometers to meters) and dividing by 3,600 (to convert hours to seconds), which simplifies to 20/3 meters per second. Finally, dividing the distance of 100 meters by this speed of 20/3 meters per second gives 15 seconds.

Step-by-Step Solution

Convert the speed of the scooter from miles per hour to kilometers per hour.

The speed is

24

kilometers per hour.

Since

1\text{ mile} = 1.6

kilometers, we multiply

15

1.6

to find the speed in kilometers per hour.

Convert the speed from kilometers per hour to meters per second.

The speed is

\frac{20}{3}

meters per second.

There are

1,000

meters in

1

kilometer and

3,600

seconds in

1

hour. Thus, the speed is

\frac{24 \times 1,000}{3,600} = \frac{20}{3}

meters per second.

Calculate the time required to travel

100

meters.

The time is

15

seconds.

Using the formula

\text{time} = \frac{\text{distance}}{\text{speed}}

, we divide

100

meters by the speed of

\frac{20}{3}

meters per second:

100 \div \frac{20}{3} = 15

seconds.

Key Concept

Converting compound units and applying rate formulas to solve for time.

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