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# I'm stuck :(

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My trip to work is 120 miles. If I go 8 mph faster than my usual speed, I'll get to work 30 minutes earlier. How long does my trip take, in hours, if I go my usual speed?

and also:

What is the ratio of the width to length of a folded sheet of paper if the rectangle formed when the sheet is folded in half (as shown below) is similar to the original rectangular sheet? Express your answer as a common fraction in simplest radical form. (Assume the width of the original sheet of paper becomes the length of the folded sheet.)

Mar 20, 2021

#1
+121003
+1

My trip to work is 120 miles. If I go 8 mph faster than my usual speed, I'll get to work 30 minutes earlier. How long does my trip take, in hours, if I go my usual speed?

30 min  = 1/2  hr

Let  your usual  speed =  r

Let  the  greater  speed =  r + 8

Distance / Rate  =  Time

So

Time  at faster speed  + 1/2  hr =  Time  at normal speed.....so....

120 / (r + 8)  +   1/2   =   120 / r  rearrange  as

1/2  =   120/r  -  120/ ( r + 8)

1/2 =  [ 120 ( r + 8)  - 120 r ]   / ( r * (r + 8) )

1/2  =  [ 120r  + 960 -120r ]  / (r ( r +8))

1/2 =    ( 960 )  / ( r (r + 8))        cross-multiply

r ( r + 8)  =  960 * 2

r^2  + 8r  =  1920

r^2  + 8r  - 1920   =  0

(r  + 48)  ( r - 40) =   0

The  second factor   set to  0  is  what we need

r -40   =   0

r  =  40 mph

Time to work at  normal speed  =   120  / r =   120  /  40 =    3 hrs

Mar 20, 2021
#2
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Then what would the answer to the second question be?

Thanks!

Mar 20, 2021