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.)
+128474 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
