Question

Bob's speed was 20 mph faster than that of Lisa. Thus Bob could travel 240 miles in 2 hrs less than it took Lisa to travel 160 miles. Find the speeds and times of both.

Answer 1

i wonder if this is right, because i get an ugly answer, so maybe i made a mistake

Answer 2

yeah it is wrong

Answer 3

bobs rate is x, lisa's is x - 20
bobs time is
\[\frac{240}{x}\] lisa's is
\[\frac{160}{x-20}\] and we know
\[\frac{240}{x}=\frac{160}{x-20}+2\] that is better

Answer 4

i get the problem until i plug it into the equation Distance=Time x Rate. After i plug in the information it makes no sense.

Answer 5

maybe it would make more sense if we tried it with numbers

Answer 6

suppose lisa's speed is 40
then bob's speed has to be 60

Answer 7

i use bob's time x bob's rate = 240 miles
then (lisa's rate -20) x (lisa's time +2) = 240 miles if i substitue the given information.
after this point i get stuck

Answer 8

lol satellite for some reason I read bobs as boobs 4 times.. and i was thinkin what the heck are these guys doing!

Answer 9

at 60, bob would take 240/60= 4 hours
lisa would take 160/40 = 4 hours. so their time would be equal

Answer 10

lol

Answer 11

haha

Answer 12

how do you know bob's rate? it just says that it is 20 greater than lisa's

Answer 13

ok lets go slow

Answer 14

i don't know bob's rate, so i put it as x
and so lisa's rate is x - 20 so far so good?

Answer 15

then we are told information about time, and time is distance over rate
so bob's time for 240 miles is
\[\frac{240}{x}\] similarly lisa's time for going 160 miles is
\[\frac{160}{x-20}\]

Answer 16

yea i got that and that bob's time is 2less than lisa's so lisa's rate is x+2

Answer 17

it says bob goes 20 mph faster than lisa. so if bob goes 40 lisa goes 20, and if bob goes 60 lisa goes 40 and if bob goes x, lisa goes x - 20

Answer 18

so now we know that bob's time is 2 hours less than lisa's time

Answer 19

so
\[\frac{240}{x}=\frac{160}{x-20}-2\]

Answer 20

yea

Answer 21

now we have to solve for x somehow

Answer 22

it is annoying that x is in the denomiator, but i do not think it can be helped

Answer 23

\[rt=160\]
\[r=\frac{160}{t}\]
\[(r+20)(t-2)=240\]
\[rt-2r+20t-40=240\]
\[160-2r+20t-40=240\]
\[-2r+20t=120\]
\[-2(\frac{160}{t})+20t=120\]
\[\frac{-320}{t}+20t=120\]
\[-320+20t^2=120t\]
\[20t^2-120t-320=0\]
\[t^2-6t-16=0\]
\[(t-8)(t+2)=0\]
\[t=8\]