The time t required to drive a certain distance varies inversely with the speed r. If it takes 4 hours to drive the distance at 40 miles per hour, how long will it take to drive the same distance at 55 miles per hour?

Question

emmamink · Answer

ok hold on

anonymous · Answer

ok

emmamink · Answer

@TheSmartOne

thesmartone · Answer

Hi, do you know what inversely proportional means?

anonymous · Answer

no.

emmamink · Answer

Omg u r an ambassador too? congrats!

thesmartone · Answer

Seem familiar?

$\sf\LARGE y=\frac{k}{x}$

anonymous · Answer

no.

emmamink · Answer

lol im gonna do trig and i dont even recognize that. i am really tired today. cant think straight....

thesmartone · Answer

y is inversely proportional to x

so then that makes

$\sf\LARGE y=\frac{k}{x}$

where k is a constant

thesmartone · Answer

The time t required to drive a certain distance varies inversely with the speed r. 

That means

$\sf\Large t = \frac{k}{r}$

thesmartone · Answer

If it takes 4 hours to drive the distance at 40 miles per hour.

Use that infomation to get the value of k

thesmartone · Answer

And then finally, plug back k into that formula and plug in the last piece of information they gave you to solve for time

how long will it take to drive the same distance at 55 miles per hour?

anonymous · Answer

2.91 hours

thesmartone · Answer

what's that?

anonymous · Answer

t = 2.91 hours.

thesmartone · Answer

they told you 

If it takes 4 hours to drive the distance at 40 miles per hour.

t there is 4

anonymous · Answer

oh.

thesmartone · Answer

but that isn't your final answer :p

thesmartone · Answer

Are you saying that t=2.91 as your final answer? @allen10

anonymous · Answer

yes

thesmartone · Answer

That is correct :)