Question 1118935
Sophie leaves Town A and cycles towards Town B, 100 km away at a speed of 5 metres per second.
 Thirty minutes later, Frank leaves Town B, travelling towards Town A, at 9m/s.
: 
a) How long has Frank been travelling when he meets Sophie.
Let t = travel time of Frank when he meets Sophie
Frank left half hour later than Sophie, therefore
(t+.5) = travel time of Sophie
:
Change the speeds to km/hr
{{{(5*3600)/1000}}} = 18 km/h
and
{{{(9*3600)/1000}}} = 32.4 km/h
" 
Write distance equation dist = speed * time,
S's dist + F's dist = 100 km
18(t+.5) + 32.4t = 100
18t + 9 + 32.4t  = 100
50.4t = 100 - 9
t = 91/50.4
t = 1.8 hrs or 1 + .8 *60 = 1 hr 48 minutes Frank traveled to meet S
: 
:
b) How many kilometres from Town A are they when they meet?
Multiply Sophie's travel time by 18 km/hr 
1.8 + .5 = 2.3 hrs
18 * 2.3 = 41.4 km from A
:
;
Check this, find the distance traveled by F
1.8 * 32.4 = 58.32 F
41.4 + 58.32 = 99.7 not quite 100 because I rounded off the time to 1.8 hrs