Question 66362
During rush hour, Fernando can drive 20 miles using the side roads in the same time it takes to travel 15 miles on the freeway. If Fernandos rate on the side roads is 9 mi/h faster than his rate on the freeway, find his rate on the side roads.
Is the answer 29?
:
Let s = his speed on the sideroads
Then (s-9) = his speed on the freeway
:
Write a time equation, time = dist/speed
side-road time = freeway time
{{{20/s}}} = {{{15/((s-9))}}}
:
Cross mult and you have:
20(s-9) = 15s
20s - 180 = 15s
20s - 15s = 180
5s = 180
s = 180/5
s = 36 mph on the side-roads
:
:
Check our solution using the time eq:
20/36 = 15/27
5/9 = 5/9 confirms our solution