Question

A salesman drives from
Ajax to Barrington, a distance of 120 mi, at a steady speed. He
then increases his speed by 10 mi/h to drive the 150 mi from
Barrington to Collins. If the second leg of his trip took 6 min
more time than the first leg, how fast was he driving between
Ajax and Barrington?

Answer 1

Please help I'm confused!

Answer 2

i am sure we can do this, let me write it down so i don't make a mistake

Answer 3

Okay thanks!

Answer 4

ok lets put the rate from A to B as \(r\)
then since time is distance divided by rate , we can write
\[t=\frac{120}{r}\] where \(t\) is the time from A to B

Answer 5

the rate from B to C is 10 more, i.e. \(r+10\) and the time is 6 more, i.e. \(t+6\) so we also have
\[t+6=\frac{150}{r+10}\]

Answer 6

then the job is to solve the two equations
\[t=\frac{120}{r}\\t+6=\frac{150}{r+10}\]

Answer 7

we can get rid of the \(t\) in the second one and write
\[\frac{120}{r}+6=\frac{150}{r+10}\]

Answer 8

wait i think i screwed this up, hold the phone

Answer 9

Oh man okay

Answer 10

Now you know why I'm confused haha

Answer 11

lol i am an idiot
it is six MINUTES not 6 hours

Answer 12

Lol exactly

Answer 13

And you're not an idiot lol

Answer 14

\[\frac{120}{r}+\frac{1}{10}=\frac{150}{r+10}\]

Answer 15

as six minutes is one tenth of an hour

Answer 16

What would be the unit for r?

Answer 17

r is a rate, it is miles per hour
t is also in hours
i changed 6 minutes to one tenth of an hour

Answer 18

so now all the units match up , miles, hours, miles per hour

Answer 19

Do you mind solving the equation, because this is actually a question from the practice test and I'm a visual learner and for me to comprehend it more clearly ill need all the help I can get please!

Answer 20

i guess we can do it
\[\frac{120}{r}+\frac{1}{10}=\frac{1200+r}{10r}\]

Answer 21

then we get
\[\frac{1200+r}{10r}=\frac{150}{r+10}\] "cross multiply" and get
\[(r+10)(1200+r)=1500r\]

Answer 22

multiply out, set it equal to zero and solve
you get
\[r^2-290r+12000=0\] and by some miracle this factors as
\[(r-50)(r-240)=0\]

Answer 23

so either \(r=50\) or \(r=240\)
i think we should pick 50

Answer 24

then we still have to find the time from A to B but now that is easy, as it is distance divided by rate, which is \(\frac{120}{50}=2.4\) or two hours and 24 minutes

Answer 25

i have to say this was a pain, and there may have been a shorter way to do it, but i don't see it

Answer 26

Lol it's okay but thanks! :)

Answer 27

yw

Answer 28

So how would I know I'll have to put the distance over r?