Not really an article, just solving some readers’ queries to keep the STD concept refreshed.

# Case: Train, Man and Bridge

A man is standing on a 180m long bridge.He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed.
Approach:

 When train crosses the bridge When train crosses the man Total distance= length of train + width of bridge length of train + width of bridge “m”+180 “m”+0

Because in comparison to train, man / telephone wire / bike-rider etc are considered zero in width.
Now make table

 Train + bridge Train + man Speed “s” “s” Time 20 8 Distance M+180 M

Now apply STD formula and you get two equations

 Train + bridge Train + man Speed “s” “s” Time 20 8 Distance M+180 M Speed X time = Distance S x 20 = (M+180) S x 8 =M

Just solve those two equations
20s=M+180….(i)
8s=M….(ii)
So in first equation, replace the value of M=8s
20s=8s+180
20s-8s=180
12s=180
S=180/12
S=15 m/s. that’s our final answer. But suppose, in the answer options, the speed is given in in km/h, then you need to convert m/s into km/h.

# Conversion : kmph vs ms

1km =1000 meters.
1 hr = 60 minutes = 60 x 60 seconds = 3600 seconds.
Therefore, 1 km / hr = 1000m / 3600 seconds
1km / hr = 5 / 18 (m/s)
In otherwords,
1 meter per second = 18 / 5 kmph.
So 15 (m/s) = 15 x (18/5) km/h = 54 kmph. That’s our final answer.

# Finding length of train

Moving to the next part: find the length of this train.
From the second equation, we know that
S x 8 =M
And we’ve found that speed of train= 15m/s.
hence 15 x 8 =m
m=120meters.
Answer: length of train is 120 meters.

# Case: Time n Work : A and B

Question: A can do a piece of work in 80 days. He works at it for 10 days and then B alone finishes the remaining work in 42 days. In how much time will A and B together finish the work?
Make table

 A B Speed a b Time 80 b Distance = speed x time a x 10=80a

It means total distance to be covered, is “80a”.

## A works for 10 days

 A B A works Speed a b a Time 80 10 Distance = speed x time a x 10=80a 10 x a =10a

See the last column. A covered distance of 10a, meaning
So 80a-10a=70a distance is yet to be covered.
Now B comes and finishes this in 42 days

 A B A works B finishes Speed a b a b Time 80 10 42 Distance = speed x time a x 10=80a a x 10 =10a. (meaning 70a remains). b x 42= 42b

That means 42b=70a (because remaining work =70a and B finished this.)
b=(70/42)a
Therefore, b=5a/3
Now if A+B worked together then, we can add their speed. And together they’ve to finish 80a distance

## Update the table

 A B A works B finishes A+B together Speed a b=5a/3 a b a+5a/3=8a/3 Time 80 10 42 T Distance = speed x time a x 10=80a a x 10 =10a. (so 70a work remains). b x 42= 42b 80a

Apply STD in last column
Speed x time = distance
8a/3 x T =80a
Therefore T= 30 days.
Final answer: if A and B work together, it’ll take them 30 days to finish the job.