Ellen is at a hydroplane boat show starting from 1.0 miles away the boat drives toward her and then passes her the boat travels at a constant rate of 70 miles per hour the distance of the boat from ellen is given by d=|1.0-70t| at what time is the boat 0.15 miles from ellen calculate your answers in seconds.

Answer choices:

A: 42 seconds and 61 seconds
B: 40 seconds and 50 seconds
C: 437 seconds and 591 seconds
D: 43.7 seconds and 59.1 seconds

Question

Ellen is at a hydroplane boat show starting from 1.0 miles away the boat drives toward her and then passes her the boat travels at a constant rate of 70 miles per hour the distance of the boat from ellen is given by d=|1.0-70t| at what time is the boat 0.15 miles from ellen calculate your answers in seconds.

Answer choices:

A: 42 seconds and 61 seconds
B: 40 seconds and 50 seconds
C: 437 seconds and 591 seconds
D: 43.7 seconds and 59.1 seconds

phi · Answer

they want you to solve 
|1.0-70t| = 0.15

t will be in hours, so you will have to multiply by 60 to change the answers to minutes
and then by 60 again to change the answer to seconds.

But first, do you know how to solve for "t" ?

dutchess101 · Answer

I don't believe so.

dutchess101 · Answer

Would I do 1.0-1.0 which crosses out then 0.15-1 which is -0.85?

phi · Answer

the absolute value has two solutions.  if what is "inside" is positive, we drop the absolute value, and solve "normally"

so the first solution begins by writing
|1.0-70t| = 0.15
as
1.0-70t = 0.15

to "solve for t", I would first add -1 to both sides, like this:
1.0 - 1.0 -70t = 0.15 - 1.0

now simplify both sides. can you do that ?

dutchess101 · Answer

Okay so would I do 1.0-1.0= cross out and 0.15 -1.0 = -0.85 and be left with -70t = -0.85

phi · Answer

yes
now divide both sides by -70

dutchess101 · Answer

Okay I got 
t = 0.0121428571428571

phi · Answer

you get
$$ t = \frac{0.85}{70} $$
that will be in hours.
the answers are in seconds, so we should multiply by 60*60 (or 3600) 
$$t = \frac{0.85}{70} \cdot 3600 $$

dutchess101 · Answer

I got 43.714... 
 would that be correct?

phi · Answer

yes.  rounded to the nearest 10th we get 43.7 seconds

there is only 1 answer choice with that, so we can assume that is the answer.

phi · Answer

but if we wanted to find the other answer, we assume the "inside" of the absolute value is negative (the absolute value will make it positive)
we get the same effect if we drop the absolute value, but multiply by -1
in other words

|1.0-70t| = 0.15
becomes

-1*(1.0-70t) = 0.15

multiplying the -1 times each term inside the parens:
-1 + 70 t = 0.15

we now solve:  add +1 to both sides, and simplify
70 t = 1.15
divide both sides by 70
t = 1.15/70
change to seconds by multiplying by 60*60

dutchess101 · Answer

Thank you so much for all of your help and for explaining how to get the other answer as well Have a great rest of the day!