SOLUTION: Becky rides her bike to school in 20 minutes. The trip home uphill takes 30 minutes. If her rate is 8 mph faster there than trip home, what is her rate? Thanks! w

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Question 272339: Becky rides her bike to school in 20 minutes. The trip home uphill takes 30 minutes. If her rate is 8 mph faster there than trip home, what is her rate?
Thanks! wwoolaver@hotmail.com
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Becky rides her bike to school in 20 minutes.
The trip home uphill takes 30 minutes.
If her rate is 8 mph faster there than trip home, what is her rate?
:
since we are using mph, change the minutes to hrs
20 min = 20/60 = 1/3 hr
30 min = 1/2 hr
;
let r = rate up hill
then
(r+8) = rate down hill
:
Dist to and from is the same, write a dist equation: dist = time * rate
:
dist home = dist to school
1%2F2r = 1%2F3(r+8)
Multiply by 6, results
3r = 2(r+8)
:
3r = 2r + 16
:
r = 16 mph is the rate home
and
16 + 8 = 24 mph the rate to school
:
:
Check solution by finding the distances (should be the same)
1%2F2*16 = 8 mi
1%2F3*24 = 8 mi