Question

What is the length of the bridge which a man riding 15km an hour can cross in 5 minutes?
A) 850m
B) 1050m
C) 1250m
D) Can’t be determined

Answer 1

Hint: Substitute the values given, in the formula of speed in terms of distance and time. Convert the speed given in kilometers per hour into meters per second. Also convert the asked time into seconds so that all will be in the same units. Now find the distance using the formula in meters. The formulae we can use in this question is 1km=1000m ,1hr=60 minutes, 1 minute=60 seconds and $speed = \dfrac{{dis\tan ce}}{{time}}$


Complete step-by-step answer:
Given that the speed is 15km/h

We need to convert the speed from kmph to m/s in order to make all the units equal of a given dimension

We know that 1km=1000m and 1hr=60 minutes and 1 minute=60 seconds;

$\eqalign{
  & 1\dfrac{{km}}{h} = \dfrac{{1000m}}{{(60 \times 60)s}}; \cr
  & \,\,\,\,\,\,\,\,\,\,\, = \,\dfrac{5}{{18}}m/s \cr} $

$ \Rightarrow 1km/h = \dfrac{5}{{18}}m/s;$

$ \Rightarrow $ 15km/h=15$ \times \dfrac{5}{{18}}$m/s=$\dfrac{{25}}{6}m/s$
Given that he crosses the bridge by 5 minutes,

So now, by converting minutes into seconds we get,

5 minutes=5$ \times 60\sec onds = 300\sec onds$

We know that the formula of speed is
$speed = \dfrac{{dis\tan ce}}{{time}}$ ;

$ \Rightarrow $ $\dfrac{{25}}{6}m/s$=$\dfrac{{length\,of\ bridge}}{{Time\,taken\,to\,cross\,the\,bridge}}$ ;

Now let us suppose that the length of the bridge is d meters;

$ \Rightarrow \dfrac{{25}}{6}m/s$=$\dfrac{d}{{300}}$ ;

$ \Rightarrow $d = 1250 meters

Hence, the length of the bridge is 1250 m.

So, the correct answer is “Option C”.

Note: Make sure to check all the units properly and convert it according to question. And check the calculations twice while doing this question. We can also solve the question by converting all the units in terms of kilometers and hours but make sure to change the last answer into meters from kilometers while doing it in this model.