SOLUTION: In a 75 m race if ace gives flash a 15 m head start, ace and flash will tie. If flash gives speedy a 15 m head start, flash and speedy will tie. At these rates how many meters head

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Question 544056: In a 75 m race if ace gives flash a 15 m head start, ace and flash will tie. If flash gives speedy a 15 m head start, flash and speedy will tie. At these rates how many meters head start should ace give speedy for ace and speedy to tie in a 75 m race?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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In a 75 m race if ace gives flash a 15 m head start, ace and flash will tie.
If flash gives speedy a 15 m head start, flash and speedy will tie.
At these rates how many meters head start should ace give speedy for ace and speedy to tie in a 75 m race?
:
Let's assign a speed to Ace, 10 m/sec, then find Flashe's speed
:
Write a time equation, time = dist/speed, let f = Flashe's speed
a's time = f's time
75%2F10 = 60%2Ff
Cross multiply
75f = 10*60
f = 600%2F75
f = 8 m/sec is Flashes speed
:
Do the same with Flash and speedy
f's time = s's time
75%2F8 = 60%2Fs
75s = 8*60
s = 480%2F75
s = 6.4 m/sec is Speedy's speed
:
Write a time equation for Ace and Speedy
let d = distance covered by speedy while Ace covers 75 m
75%2F10 = d%2F6.4
10d = 75*6.4
10d = 480
d = 48 meters
therefore
Ace should give Speedy 75-48 = 27 m head start for them to finish at the same time