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?
:
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
{{{75/10}}} = {{{60/f}}}
Cross multiply
75f = 10*60
f = {{{600/75}}}
f = 8 m/sec is Flashes speed
:
Do the same with Flash and speedy
f's time = s's time
{{{75/8}}} = {{{60/s}}}
75s = 8*60
s = {{{480/75}}}
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
{{{75/10}}} = {{{d/6.4}}}
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