Your mother takes you to your grandparents house for dinner. she drives 60 minutes at a constant speed of 40 miles per hour. she reaches the highway, quickly speeds up, and drives another 30 minutes at constant speed for 70 miles per hour. how far did you and your mother travel altogether? how long did the trip take?

Step-by-step explanation:

We will separate our trips as "slow" and "fast".  Filling in a motion table:

              d        =        r        x        t

slow

fast

We know that the slow rate is 40 mph and the time is, in hours (because the time has to match the rate.  We can't say "40 mph" and then state the time in minutes), 1 hour.

We know that the fast rate is 70 mph and the time in hours is .5 hours.

If distance = rate times time, then the distance traveled at the slow speed is 40 * 1 = 40 miles

The distance traveled at the fast speed is 70 * .5 = 35 miles.

The trip was 40 + 35 = 75 miles total, and the time it took was 1 + .5 = 1.5 hours.

let m = monomial

let t = trinomial

so, m times t = t.

monomial times a trinomial = another trinomial.