SOLUTION: Sophie leaves Town A and cycles towards Town B, 100km away at a speed of 5 metres per second. Thirty minutes later, Frank leaves Town B, travelling towards Town A, at 9m/s. a) Ho

Question 1118935: Sophie leaves Town A and cycles towards Town B, 100km 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
b) How many kilometres from Town A are they when they meet?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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
= 18 km/h
and
= 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
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