Question

Is this a trick question?

"You travel 10 miles on your bicycle in the same amount of time it takes your friend to travel 8 miles on his bicycle. If your friend rides his bike 2 mi/h slower than you ride your bike, find the rate at which each of you is traveling."

Answer 1

no, it sounds like an algebra problem

Answer 2

D=R(T)
D=Distance
R=rate
T=Time

There is not enough information in the equation to complete and solve the formula above. Also, The first sentance says "You travel 10 miles on your bicycle in the same amount of time it takes your friend to travel 8 miles."
It says your friends rides his bike 2 miles slower than you. (10-8=2) And so the restrictions are met. They are asking you to find the rate, but it's in the first sentence. Is this a trick question, or am I just crazy?

Answer 3

Looking at my above post, are you sure?? @phi

Answer 4

we have
r1 * t = 10
r2 * t = 8
where r1 is rate1 and r2 is rate2. t is the *same time*
so we can say

t= 10/r1
t= 8/r2
and
10/r1 = 8/r2

now use
If your friend rides his bike 2 mi/h slower
that means r2 is ?
can you finish ?

Answer 5

I got x= 4/5?

Answer 6

you said
**It says your friends rides his bike 2 miles slower than you. (10-8=2) **

don't get confused. rate is miles per hour and they did not tell you either rate

if you were going 20 miles per hour and he were going 18 miles per hour
then the difference in rates is 2 miles per hour.

Answer 7

Okay, I thought you might say that. :) So is r2=4/5 right?

Answer 8

I got x= 4/5?

you should say what x is. But no, neither rate is 4/5 miles per hour (0.8 miles per hour)

if your rate is r1 and his is r2
what is r2 compared to r1 ?
use your friend rides his bike 2 mi/h slower

Answer 9

in other words rides his bike 2 mi/h slower than r1
or r2 is slower than r1 by 2 mile per hour
or r2 = ?

Answer 10

So...Then r1=10, r2=8

Answer 11

well, it would be nice to see the algebra.

you should ponder how the words
rides his bike 2 mi/h slower than r1

are translated into
or r2 is slower than r1 by 2 mile per hour
or r2 = r1 - 2

now replace r2 with r1-2 in
10/r1 = 8/r2

to get
10/r1 = 8/(r1-2)

solve for r1
one way is cross multiply

Answer 12

Haha- Noted, include algebra. :) but just so you know, that is how I got my answer. Thank you for looking at this for me. I really appreciate it. :)