Given
Alvin runs 2 km to the bus stop, and then rides 4.5 km to school.
the bus is 45 km/h faster than Alvin’s average running speed
entire trip takes 25 min,
Find
how fast does Alvin run?
Explanation
Let r be the running speed of Alvin
so , bus speed = 45 + r
time = distance/speed
run time + ride time = entire time
so ,
[tex]\begin{gathered} \frac{2}{r}+\frac{4.5}{45+r}=\frac{25}{60} \\ \\ \frac{2(45+r)+4.5r}{r(45+r)}=\frac{5}{12} \\ \end{gathered}[/tex]on solving this , we get
[tex]\begin{gathered} 5r^2+147r-1080=0 \\ r=6.0868,-35.48677 \end{gathered}[/tex]as we neglect the negative value ,
so , r = 6.0868
Final Answer
Hence , the Alvin speed = 6.0868 approx