Question 408347
Mei runs an 18-mile course at constant speed.
 If she doubles her usual speed, she can compete the course in an hour and a half less than her usual time. 
What is Mei's usual speed and her usual time to compete the course?
:
Change 1 hr and a half to 1.5 hrs
:
Let s = the normal speed
then
2s = double the normal speed
:
Write a time equation, Time = dist/speed
:
Usual time - faster time = 1.5 hrs
{{{18/s}}} - {{{18/(2s)}}} = 1.5
multiply by 2s to clear denominators, results:
2(18) - 18 = 2s(1.5)
36 - 18 = 3s
18 = 3s
s = {{{18/3}}}
s = 6 mph is the usual speed
:
Find the usual time
{{{18/3}}} = 3 hrs is the usual time
:
:
Check solution by finding the time at the faster speed (12 mph)
{{{18/12}}} = 1.5 hrs, which is 1.5 hrs faster than the usual time of 3 hrs