Question

please help with 2 questions! will give medal and become fan!

Answer 1

1. Heather leaves on a long trip driving at a steady rate of 40 miles per hour. her sister Megan leaves from the same location traveling to the same destination 3 hours later. she drives at a steady rate of 50 miles per hour. how long after Megan leaves home will she catch up to heather?

2. you drop a rock off a bridge. the rocks height h (in feet above the water), after t seconds is modeled by h = -16t2 + 568. what is the height of the rock after 4 seconds

Answer 2

for 2nd question put t=4 in your equation
so h=-16*16+568=312 feet

Answer 3

do you know 1?

Answer 4

let us suppose A to B is the distance travelled by heather in 3 hours.
so Distance = speed*time
AB=40*3=120 miles
additionally, suppose BC is the distance travelled by both heather and megan and both meet together at point C.

Answer 5

As heather and megan is going to travel the same distance upto point C.
So,when distance is constant, we have
\[\frac{ S1 }{ S2 }=\frac{ T1 }{ T2 }\]
where S1,S2,T1,T2 are speeds and times taken by heather and megan.
if we take left hand sideS1/S2
\[\frac{ 50 }{ 40 }=\frac{ 5 }{ 4 }\]
which means \[\frac{ T1 }{ T2 }=\frac{ 5 }{ 4 }\]

Answer 6

so it means when heather travels 4m by the same time megan travels 5m distance.
so we can say that BC=4 and AC=5
which implies AB=1
(all these AB,AC and BC are in ratios,so if i'm saying AB=1 and BC=4 then this means AB:BC::1:4)
we know, when AB=1 then BC=4
but AB=120 miles
so when AB=120 then BC must be 120*4=480 miles
then AC=480+120=600 miles.
So, Megan will catch up to heather by 600 miles.