SOLUTION: Erica noted that a train to Muizenberg took 8 minutes to pass her. A train in the opposite direction to Cape Town took 12 minutes to pass her. The trains took 9 minutes to pass eac

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Question 922500: Erica noted that a train to Muizenberg took 8 minutes to pass her. A train in the opposite direction to Cape Town took 12 minutes to pass her. The trains took 9 minutes to pass each other. Assuming each tram mamtained a constant speed, and given that the train to Cape Town was 150m long, what was the length of the train to Muizenberg? (15)
Answer by ankor@dixie-net.com(22740) (Show Source):
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Erica noted that a train to Muizenberg took 8 minutes to pass her.
A train in the opposite direction to Cape Town took 12 minutes to pass her.
The trains took 9 minutes to pass each other.
Assuming each tram maintained a constant speed, and given that the train to Cape Town was 150m long, what was the length of the train to Muizenberg?
:
Are you sure that the time intervals you give here are minutes and not seconds?
If the C.T. train was 150 m long took 12 min to pass a point, that is not even 1 km/h
However, if it took 12 sec: * = 45 km/h, a reasonable speed.
:
Let m = speed of the Muiz train in m/sec
Let L = length of the Muiz train in meters
:
Find the speed of the C.T train
150/12 = 12.5 m/sec
and likewise the Muiz train
m = L/8
Or
L = 8m
:
When the trains go toward each other, the relative speed = m + 12.5
The lengths of both trains is added together: L + 150
= 9 sec
replace L with 8m
= 9 sec
therefore
8m + 150 = 9(m+12.5)
8m + 150 = 9m + 112.5
150 - 112.5 = 9m - 8m
m = 37.5 m/sec the speed of the Muiz train
Find the length of the train
8(37.5) = 300 meters length of the Muiz train