Is the Time Required to Travel D Miles at S MPH the Same as D/2 Miles at 2S MPH?

[bobsmith76]

which is greater or are they equal

1) the time required to travel d miles at s miles per hour

or

2) the time required to travel d/2 miles at 2s miles per hour


I thought 1) is equivalent to d*s or ds

and I thought 2) is equivalent to

d/2 * 2s

which simplifies to

ds

so they're the same but my book says 1) is greater

 

[pwsnafu]

Suppose Adam travels at 10 mph. He wants to travel 40 miles. How long will it take him?
Suppose Bob travels 20 mph. He wants to travel 20 miles. How long will it take him?

 

[cepheid]

The problem you're having here is that the time required to travel distance d at speed s is d/s, not d*s.

 

[Mentallic]

d/s = t, so rearranging this we get d = st

If the options were instead:

1) the distance traveled after t hours at s miles per hour

2) the distance traveled after t/2 an hour at 2s miles per hour

Then they would be equal, because using the rearranged equation we have

1) d = s*t
2) d = 2s*t/2 = s*t

Oh and by the way, to remember this equation, it should just be intuitive but if you can't do that, think about the units! Distance is measured in miles (or equivalent), time is measured in hours, and speed is measured in miles/hour. So from this you can quickly tell that speed = distance / time since miles per hour means miles / hours.

 

[CellCoree]

I would like to clarify that both expressions represent the same amount of time required to travel a certain distance. Therefore, they are equal. The expressions may look different, but they are mathematically equivalent. It is possible that the book may have made a mistake in stating that 1) is greater. I would suggest double-checking the calculations and equations to ensure accuracy.