I am a desperate parent trying to help my 15 year old daughter with word problems. One in particular has stumped us, so any feedback would be appreciated at this point. Here's the question:
Two girls went on a run. Cary began running 40 seconds earlier than Kristie.
*Cary ran at a speed of 10 feet per second
*Kristie ran at a speed of 12 feet per second
How many seconds had Cary been running at the moment when the two girls had ran exactly the same distance?
Thanks in advance!
Let us denote Cary and Kristie by C and K for ease of calculations.
It is given that Cary has a speed of 10 ft/s and Kristie is running at 12 ft/s
i.e., Vc = 10 ft/s and Vk = 12 ft/s
Also, if tc and tk are the times for which Cary and Kristie had been running, respectively.
we know that tc = tk + 40
(since Cary began running 40 seconds earlier).
or, tk = tc- 40
Now, distance traveled = speed x time
when both Cary and Kristie had run the same distance,
Vc x tc = Vk x tk
or, 10 x tc = 12 x (tc-40)= 12 tc - 480
or, 12 tc- 10 tc = 480
or 2 tc = 480
or, tc = 480/2= 240 seconds.
i.e. Cary had been running for 240 seconds when they have traveled the same distance.
lets us do a quick check,
Time for which Cary had been running = 240 sec
Time for which Kristie had been running = tc-40 = 200 sec
Distance traveled by Cary = 10 ft/s x 240 sec = 2400 ft
Distance traveled by Kristie = 12 ft/s x 200 s = 2400 ft
Since the distance traveled is same, hence Cary had been running for 240 seconds.
Hope this helps.