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.