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Question Number 202300 by hardmath last updated on 24/Dec/23
  Parvin leaves home to go to school. After walking 3/8 of the way, he remembers that he forgot his book. He goes back home, picks up his book, and arrives at school at the time he was originally supposed to. How many times did Parvin increase his initial speed to reach school on time ?
$$ \\ $$Parvin leaves home to go to school. After walking 3/8 of the way, he remembers that he forgot his book. He goes back home, picks up his book, and arrives at school at the time he was originally supposed to. How many times did Parvin increase his initial speed to reach school on time ?
Answered by mr W last updated on 24/Dec/23
he walked 2×(3/8)=(3/4) more way than   usually, i.e. 1+(3/4)=(7/4) times way as  usually. to reach the school in the  same time, his speed must be also  (7/4) times as usually.
$${he}\:{walked}\:\mathrm{2}×\frac{\mathrm{3}}{\mathrm{8}}=\frac{\mathrm{3}}{\mathrm{4}}\:{more}\:{way}\:{than}\: \\ $$$${usually},\:{i}.{e}.\:\mathrm{1}+\frac{\mathrm{3}}{\mathrm{4}}=\frac{\mathrm{7}}{\mathrm{4}}\:{times}\:{way}\:{as} \\ $$$${usually}.\:{to}\:{reach}\:{the}\:{school}\:{in}\:{the} \\ $$$${same}\:{time},\:{his}\:{speed}\:{must}\:{be}\:{also} \\ $$$$\frac{\mathrm{7}}{\mathrm{4}}\:{times}\:{as}\:{usually}. \\ $$

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