Question 72846
Fernando can drive 35 miles using the side roads in the same time that it takes to travel 30 miles on the freeway. If Fernando's rate on the side roads is 9 mi/h faster than his rate on the freeway, find his rate on the side roads.
:
Let s = his speed on the side roads
:
Then (s-9) = his speed on the freeway
:
Since the times are equal, write a time equation; time = dist/speed:
:
Sideroad time = freeway time
{{{35/s}}} = {{{30/((s-9))}}}
:
Cross multiply and you have:
35(s-9) = 30s
35s - 315 = 30s
35s - 30s = + 315
5s = 315
s = 63 mph on the side-road, you were close
:
:
Check to see if the times are, in fact equal. Freeway speed: 63-9 = 54 mph
30/54 = .556
35/63 = .556