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A fast train covers $320km$ in $3$ hours $20$ minutes. How much time will it take to cover a distance of $90km$.
$A)76.25$ minutes
$B)56.25$ minutes
$C)36.25$ minutes
$D)$ None of these

Last updated date: 16th Jul 2024
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Hint: First we have to define what the terms we need to solve the problem are. Since km means kilometer of the train covered distance. Now we are going to convert hour into minutes is one hour equals sixty minutes that is $1hour = 60\min $, we will convert $3$ hours $20$ minutes into the total minutes that is $3h = 180\min $ plus the twenty minutes and hence $3$ hours $20$ minutes $ = 200\min $

Complete step-by-step solution:
Since that train is traveled the total distance of $320km$(kilometer) and in the time of
$3$ hours $20$ minutes $ = 200\min $ so now we will need to find the train distance of $90km$ in what time. Let the train cover $320km$ in $200\min $ that means by division formula we can able to convert one kilometer equals the two hundred minutes; which is $1km = \dfrac{{200}}{{320}}\min $ so the train is traveled in one kilometer is $\dfrac{{200}}{{320}} = 0.625$minutes and hence we need to find now the train covered $90km$distance.
Thus , for $90km$$ = (0.625 \times 90)\min $$ = 56.25\min $ which is the train traveled ninety kilometers.
Hence option $B)56.25$minute is correct. If option $C)36.25$minute is correct then the train will travel below $320km$ in $3$hours $20$minutes. If the option $A)76.25$ minute is correct then the train will travel above $320km$in $3$hours $20$minutes. So hence options like A and C are wrong.

Note: We are also able to solve this problem without converting the hours into minutes, by just dividing the given time $3$hours $20$minutes by $320km$ and then multiplying with $90km$ to get the same result as above. Since none of these means; no options are correct but, in the problem, we get the correct option B; and hence $D)$ none of these is also wrong.