City baths

In the city baths, each visitor pays 100 Kč (Czech crown) for 90 minutes. With a city card, the visitor pays for the same time 50 Kč. The price of the city card is 300 Kč. Martin and Emil always go swimming together and their visit lasts exactly 90 minutes. Martin bought the city card, Emil did not. Martin used the card at every visit. When they last left the city baths, they found out that both had spent the same, Martin included the entire price of the card in the expense.

a) How many hours did each of the boys spend in the baths before they paid the same.
b) At what lowest possible visit M+E did Martin pay in total less than Emil.

Final Answer:

t =  9 h
b =  7

Step-by-step explanation:

$$\begin{gathered} a\cdot 100=50\cdot a+300 \\ 50a=300 \\ a=\frac{300}{50}=6 \\ a=6 \\ {t}_1=90\text{min}\to \text{h}=90:60\text{h}=1.5\text{h} \\ t=t_1\cdot a=1.5\cdot 6=9\text{h} \end{gathered}$$

$b=a+1=6+1=7$

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