Question

Reason Abstractly Explain why a

student who runs 3/4 mile in 6 minutes is faster than a student who runs 1/2 mile in 5 minutes.

Answer 1

3/4 = 0.75

1/2 = 0.5

Student A runs 0.75 miles in 6 minutes. Their speed is

distance/time = 0.75/6 = 0.125 miles per minute

Student B runs 0.5 miles in 5 minutes, so their speed is

distance/time = 0.5/5 = 0.1 miles per minute

Student A has the slightly faster speed.

Answer 2

Explanation:

Givens

Student A

d = 3/4 mile

t = 6 minutes

Student B

d = 1/2 mile

t = 5 minutes

Note

In both cases, the units are the same, so unit conversion is not necessary.

Solution

Student A

r = d / t

r is the rate of travel in miles / minute

r = 3/4 / 6

r = 3.4 // 6/1 The 1 is put below the 6 so it is easier to divide. Invert the bottom and multiply.

r = 3/4 * 1/6

r = 3/24

r = 1/8 miles / minute

Student B

r = d / t

r = 1/2 // 5 / 1 Turn the bottom fraction upside down and multiply

r = 1/2 * 1/5

r = 1/10

Question

which is bigger: 1/8 or 1/10?

1/8 = 0.125

1/10 = 0.1

1/8 is bigger by 0.025

Answer

Student A is faster by 0.025 miles / minute.