Question 141976: At 8.15a.m, a van started from Town X heading for Town Y at a constant speed of 50km/h. Half an hour later, a lorry passed Town X also heading towards Town Y at a constant speed of 70km/h
(a) At what time would the lorry catch up with the van?
(b) If the lorry reached Town Y at 1.45pm, what is the distance between the 2 towns?
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
Let t be the number of hours after 8.15am that the lorry
caught up to the van.
Make this chart and put t for the van's time:
DISTANCE SPEED TIME
Van t
Lorry
The lorry's time at the instant the lorry caught up is one half
hour less than the van's time, since it started one-half hour
later. So we put "t-1/2" for the time the lorry traveled before
it caught up the van:
DISTANCE SPEED TIME
Van t
Lorry t-1/2
Now we put in the speeds of 50 and 70 km/h:
DISTANCE SPEED TIME
Van 50 t
Lorry 70 t-1/2
Now we use the formula
Distance = (Speed)(Time)
to fill in the two distances:
DISTANCE SPEED TIME
Van 50t 50 t
Lorry 70(t-1/2) 70 t-1/2
The two distances were equal at the instant when the
lorry caught up. So
50t = 70(t-1/2)
Can you solve that for t?
Answer: t = 1 3/4 hours.
That is, an hour and 45 minutes after 8.15am,
which would be 10.00am.
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(b) If the lorry reached Town Y at 1.45pm, what
is the distance between the 2 towns?
Let d = the distance between the 2 towns.
The lorry started at 8.45am (one half hour after 8.15am)
and reached town Y at 1.45pm. That is 5 hours. The
speed of the lorry was 70 km/hr.
Use distance = speed times time.
d = 70(5)
d = 350 km.
Edwin
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