Problema Solution
George Laura and Jane are running a 2 mile race. George runs twice as fast as Laura. Running at a constant pace, Laura will finish the race 10 minutes after George. If Laura had a 5 minute head start, she and Jane would finish at the same time. How long of a lead can George give Laura and jane so that he does not lose?
Answer provided by our tutors
we can calculate the time it takes George to run the race by letting 'v' represent George's running velocity and 't' represent George's time in minutes:
distance = velocity * time
d = vt
Laura runs half the speed of George (v/2) and takes 10 minutes longer than George (t+10)
they both run 2 miles, so we set their 'vt' expressions equal:
vt = (v/2)(t+10)
which solves to t=10
so it takes George 10 minutes to run the 2 miles and Jane finishes 5 minutes faster than Laura, therefore George finishes 5 minutes ahead of Jane (and it takes Jane 15 minutes to run the 2 miles)
if George gives them a 5 minute head start, then he and Jane would tie, so he must give something less than a 5 minute head start