Question

a car travels 2 5/8 miles in 3 1/2 minutes at a constant speed. Write an equation to represent the distance, d, that the car travels in m minutes.

Answer 1

The distance traveled, d, as a function of time, m is d = (3/4 mile/min)m

Explanation:

Recall that distance = speed times time.

Symbolically, d = r*t, where r = speed and t = time. In this problem d = r*m, where m = elapsed time in minutes.

First find the speed. Dividing 2 5/8 miles by 3 1/2 minutes yields the unit rate of travel:

2 5/8 miles

-----------------------

3 1/2 minutes

Converting both mixed numbers into improper fractions, we get:

21/8

------- miles/min

7/2

Recall that dividing by a fraction is equivalent to multiplying by the reciprocal of the divisor fraction:

21 2

------ * ------ miles/min This readily reduces to 3/4 mile/min

8 7

and so the desired equation for distance as a function of time is

d = (3/4 mile/min)m, where m is the number of minutes elapsed.

Answer 2

d = (3/4)*m

Explanation:

In 3 1/2 minutes it travels 2 5/8 miles

3 1/2 = 3.5 minutes

2 5/8 =2.625 miles

to find out how much it travels in only one minute, we divede 2.625 miles by 3.5 minutes

2.625/3.5 = 0.75 miles/minute

so, to find out how much miles it travels on m minutes, we multiply m by 0.75

distance d = 0.75 *m

or expressing this as a fraction (since 0.75 = 3/4):

d = (3/4) * m