Question

Rahul can finish one-fifth of his homework in one hour. Neha can finish three-sevenths of her homework in one hour thirty minutes and Riya can finish three fourth of her homework in three hours thirty minutes. If all of them start their homework at $12.00p.m$ and can go to play as soon as they all finish their homework, when can they start to play if they take a break at $3.30p.m$ for thirty minutes?

Answer 1

Given,

Rahul can finish $\frac{1}{5}$ of his homework in $1\mathrm{hour}.$

So, the time needed to complete his full homework $=1÷\frac{1}{5}=5\mathrm{hrs}$

Neha can finish $\frac{3}{7}$ of his homework in $1\mathrm{hour}30\min =1\frac{1}{2}=\frac{3}{2}\mathrm{hrs}$

So, the time needed to complete her full homework $=\frac{3}{2}÷\frac{3}{7}=\frac{7}{2}\mathrm{hrs}=3\frac{1}{2}\mathrm{hrs}=3\mathrm{hr}30\min$

Riya can finish $\frac{3}{4}$ of his homework in $3\mathrm{hour}30\min =3\frac{1}{2}=\frac{7}{2}\mathrm{hrs}$

So, the time needed to complete her full homework $=\frac{7}{2}÷\frac{3}{4}=\frac{14}{3}\mathrm{hrs}=4\frac{2}{3}\mathrm{hrs}=4\mathrm{hr}40\min$

All of them began their homework at $12.00\mathrm{p}.\mathrm{m}$ and they take a break at $3.30\mathrm{p}.\mathrm{m}$ for $30\min$

As Neha is taking $3\mathrm{hrs}30\min$ to finish the homework, that implies she can start to play at

$12\mathrm{p}.\mathrm{m}+3\mathrm{hrs}30\min =3:30\mathrm{p}.\mathrm{m}$ ( No break needed )

Rahul can start to play at

$12\mathrm{p}.\mathrm{m}+5\mathrm{hrs}+30\min \mathrm{break}=5:30\mathrm{p}.\mathrm{m}.$

Riya can start to play at

$12\mathrm{p}.\mathrm{m}+4\mathrm{hrs}40\min +30\min \mathrm{break}=5:10\mathrm{p}.\mathrm{m}$

Hence, Rahul can start to play at $5:30pm$, Neha can start to play at $3:30pm$ and Riya can start to play at $5:10pm$