Question

At the railway station





(a) What time is the train expected to come today?
(b) Nazia gets off at a station after $2\frac{1}{2}$ hours from this station. What time will she get off?
(c) Shaji will take 5 hours to reach Ernakulam by this train. At what time will he reach there?

Answer 1

a) The correct time for the arrival of the train is quarter to 7

= $6\frac{3}{4}$ hrs

But, the train is late by half an hour.

So, expected time of the arrival of the train = $6\frac{3}{4}+\frac{1}{2}$

= $\frac{27}{4}+\frac{1}{2}$

= $\frac{27}{4}+\frac{1\times 2}{2\times 2}$ = $\frac{27}{4}+\frac{2}{4}$

= $\frac{29}{4}$

= $7\frac{1}{4}$

Thus, the expected time of the arrival of the train is quarter past 7.


b) Expected time of the arrival of the train = $7\frac{1}{4}$ hrs

Nazia gets off at a station after $2\frac{1}{2}$ hrs of boarding the train.

Time at which Nazia will get off = $7\frac{1}{4}+2\frac{1}{2}$

= $\frac{29}{4}+\frac{5}{2}$

= $\frac{29}{4}+\frac{5\times 2}{2\times 2}$

= $\frac{29}{4}+\frac{10}{4}$

= $\frac{29+10}{4}$

= $\frac{39}{4}$

= $9\frac{3}{4}$

Thus, Nazia will get off from the train at quarter to 10.

c) Shaji will reach Ernakulam by this train after 5 hours.

Expected time of the arrival of the train = $7\frac{1}{4}$hrs

Expected time at which Shazi will reach Ernakulam = $7\frac{1}{4}+5$

= $\frac{29}{4}+\frac{5}{1}$

= $\frac{29}{4}+\frac{5\times 4}{1\times 4}$

= $\frac{29}{4}+\frac{20}{4}$

= $\frac{29+20}{4}$

= $\frac{49}{4}$

= $12\frac{1}{4}$

Thus, Shazi will reach Ernakulam at quarter past 12.