Arithmetic

Time, Speed & Distance

Medium

A train running between two towns arrives at its destination 10 minutes late when it goes at 60 km per hour and 16 minutes late when it goes at 40 km per hour. Determine the speed at which the train reaches on time.

100 km/h

360 km/h

90 km/h

240 km/h

✅ Correct Option: 2

Let the distance be $d$ km and the time needed to reach exactly on time be $t$ hours.

Minutes must be changed to hours since speed is in km per hour.

$10$ minutes $= \dfrac{10}{60} = \dfrac{1}{6}$ hour

$16$ minutes $= \dfrac{16}{60} = \dfrac{4}{15}$ hour

Time taken $=$ on-time duration $+$ delay:

$\dfrac{d}{60} = t + \dfrac{1}{6}$

$\dfrac{d}{40} = t + \dfrac{4}{15}$

Subtracting the first equation from the second removes $t$ :

$\dfrac{d}{40} - \dfrac{d}{60} = \dfrac{4}{15} - \dfrac{1}{6}$

$\dfrac{3d - 2d}{120} = \dfrac{8 - 5}{30}$

$\dfrac{d}{120} = \dfrac{1}{10}$

$d = 12$ km

$t = \dfrac{12}{60} - \dfrac{1}{6}$

$= \dfrac{1}{5} - \dfrac{1}{6}$

$= \dfrac{1}{30}$ hour

Speed to reach on time $= \dfrac{d}{t}$

$= 12 \div \dfrac{1}{30}$

$= 12 \times 30$

$= 360$ km/h

Therefore, the train reaches on time at $360$ km/h.

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