Question

During a family trip, you share the driving with your dad. At most, you are allowed to drive for three hours. While driving, your maximum speed is 55 miles per hour.
a) Write a system of inequalities describing the possible numbers of hours t and distance d you may have to drive.
b) Is it possible for you to have driven 160 miles?

Answer 1

@jim_thompson5910

Answer 2

@Vocaloid

Answer 3

@amistre64

Answer 4

@dan815

Answer 5

hopefully you recall that

distance = speed * time

agreed?

Answer 6

I agree

Answer 7

let
d = distance
r = rate or speed
t = time

Answer 8

Ok

Answer 9

"While driving, your maximum speed is 55 miles per hour"

so `r <= 55`. The value of r must be smaller than or equal to 55 mph

Answer 10

Ok

Answer 11

In addition, `r >= 0` because we can't have a negative speed

Answer 12

Ok

Answer 13

` At most, you are allowed to drive for three hours`

telling us that `t <= 3`. For similar reasons as above, `t >= 0` as well

Answer 14

Ok

Answer 15

so we have this so far

r <= 55
r >= 0
t <= 3
t >= 0

let's see. what else is there

Answer 16

b) Is it possible for you to have driven 160 miles?

Answer 17

if your max speed is 55 mph and the max amount of time is 3 hrs, then

d = r*t
d = 55*3
d = 165

so the max distance possible is 165 miles. It's definitely possible to drive 160 miles

Answer 18

Thank you so much!

Answer 19

np